The team said Happ was taken to Bayfront Medical Center, where he was alert and undergoing tests. Nursing supervisor Natasha Keller told The Associated Press that Happ had been admitted to the hospital and was in stable condition.
"I think the last indication was that he was alert and feeling better and had gone for a CT scan. That's the last I heard," Toronto pitcher R.A. Dickey said.
In a frightening scene at Tropicana Field, Desmond Jennings' second-inning liner caromed squarely off the left side of Happ's head with a loud "thwack!" that could be heard up in the press box.
The ball went all the way into the bullpen in foul territory halfway down the right-field line. Happ dropped face down at the front of the mound, holding his head with his glove and bare hand.
Jennings ended up on third base with a two-run triple. Team trainers, paramedics and medical officials rushed to Happ's aid as Tropicana Field fell into a hush.
"It's devastating. ... I could barely watch it," Dickey said. "You just don't know what to think, really. It paralyzes you a little bit. And when it sounds like two bats, when you hear the sound off the bat and it sounds like it hits another bat, it's scary. It's really, really scary. I just started praying in the spot. That's all I knew to do."
Jennings stood with his hands on his head, and other players were visibly concerned as they watched Happ receive medical attention for about eight minutes.
Jennings left the clubhouse without speaking to reporters.
Toronto manager John Gibbons stood on the mound as Happ was strapped to a backboard and immobilized. The left-hander was lifted onto a stretcher and wheeled off the field through an opening behind home plate.
"That was a real scary moment," Rays manager Joe Maddon said. "That was awful. I hope that he's well."
Just before he disappeared under the stands, Happ raised his right hand and waved. He received a standing ovation from the crowd, and the game resumed after an 11-minute delay.
Happ's injury was the latest to a pitcher struck by a batted ball during the last few years, and Major League Baseball has discussed ways to protect hurlers on the mound.
"We are actively meeting with a number of companies that are attempting to develop a product, and have reviewed test results for several products," MLB spokesman Pat Courtney told the AP in an email after Happ was injured Tuesday night. "Some of the products are promising. No company has yet developed a product that has satisfied the testing criteria."
Oakland right-hander Brandon McCarthy was hit in the head by a line drive last September, causing a skull fracture, an epidural hemorrhage and a brain contusion that required surgery. He was released from the hospital six days later.
Not long after Happ was injured Tuesday night, McCarthy's wife, Amanda, tweeted: "Thoughts go out to Happ and his family. Such a scary moment."
Major league general managers discussed the issue during their meetings in November and MLB presented several ideas at baseball's winter meetings only weeks later.
MLB staff have said a cap liner with Kevlar, the high-impact material used by military, law enforcement and NFL players for body armour, is among the ideas under consideration.
The liners, weighing perhaps five ounces or less, would go under a pitcher's cap and help protect against line drives that often travel over 100 mph.
MLB could implement the safety change in the minor leagues, as it did a few seasons ago with batting helmets, but would require the approval of the players' union to make big leaguers wear them.
Brad Lincoln replaced Happ, who gave up four runs — all in the second — and five hits in 1 1-3 innings.
Several players around the majors tweeted their thoughts and prayers for Happ and his family.
"Take for granted how fast this sport can be, Especially for players that close. No reaction time!" Dodgers infielder Jerry Hairston Jr. wrote.
Happ began spring training without a spot in Toronto's projected rotation. He earned a starting role when the Blue Jays left struggling Ricky Romero behind in Florida to work on mechanics when the season began.
Happ was obtained by Toronto in a trade with Houston last July 20. He was placed on the disabled list Sept. 7 and missed the rest of the season due to a broken right foot.
The Blue Jays grabbed a 6-4 lead in the ninth on Maicer Itzuris' solo homer and an RBI double by Melky Cabrera off Joel Peralta (0-2). Toronto, which trailed by three early on, tied it at 4 in the eighth on Jose Bautista's RBI double.
Toronto was coming off an 8-7 victory over the Rays on Monday night in which the Blue Jays rallied from a 7-0 deficit.
Adam Lind put the Blue Jays up 1-0 in the second on his first homer this season. Cody Rasmus cut the deficit to 4-3 on a two-run homer in the seventh.
Steve Delabar (3-1) threw two scoreless innings before Casey Janssen pitched the ninth for his ninth save. The Blue Jays have won three in a row for the first time this season.
Tampa Bay starter Roberto Hernandez went six innings, allowing one run and five hits. He had seven strikeouts and one walk.
Maddon was ejected in the second for arguing by plate umpire Marty Foster prior to Happ getting hurt.
Foster ruled that Sean Rodriguez's hand missed the plate as he tried to score from third during a slide on Jose Molina's bunt. Maddon was tossed after swiping his hand across the plate where the manager thought Rodriguez had touched it.
Foster also threw out Edwin Encarnacion after the Toronto first baseman struck out to end the ninth.
NOTES: Rays RF Ben Zobrist rejoined the team after missing two games following the death of his grandmother. ... A group of injured Toronto pitcher rehabbing at the team's complex in nearby Dunedin were at the ballpark. RHP Sergio Santos (right triceps) is scheduled to pitch in extended spring training games Thursday and Saturday, and if things go well he could join Class-A Dunedin next week. RHP Dustin McGowan (right shoulder) is pitching out of the bullpen in extended spring games and could start a rehab assignment next week. RHP Drew Hutchison (right elbow) is about three weeks away from throwing batting practice. RHP Kyle Drabek (right elbow) could be ready to throw batting practice in a week or two.