Encarnacion was on the bench Sunday when the Oakland Athletics completed a four-game sweep of the Blue Jays with a 4-2 victory. Toronto fell two games behind the AL East-leading Baltimore Orioles.
"It hurts us not having him on the team," said Blue Jays outfielder Jose Bautista, who was also chosen to the AL All-Star team, along with left-hander Mark Buehrle. "The No. 1 priority is to get him better."
The Blue Jays managed just five hits against Jeff Samardzija, who made his Oakland debut, and closer Sean Doolittle. Without Encarnacion in the lineup, Bautista doesn't have the same support.
"I'm happy to be named an All-Star," Encarnacion said. "I won't be playing. I will be working my leg to get back to the field as soon as I can."
Encarnacion was injured in the first inning of Saturday's loss after he drove in a run.
Bautista, nursing a hamstring injury, made a rare start at first base in Encarnacion's place.
"It was sore but I was able to run and make plays," Bautista said. "It shouldn't be too long before I'm back in right field."
Depending on the way things change over the next week, Bautista said he is ready to play anywhere, whether it be the outfield, first base or third base.
"Throw me in the fire," he said. "If playing third gives us our best lineup, so be it. We can't afford to be picky. We have to strap it on and do it."
The Blue Jays managed four runs during the four-game series, which included a 1-0 loss in 12 innings on Friday.
"We got shut down big time," Blue Jays manager John Gibbons said. "We had chances, it didn't happen. We're just not producing."
Stephen Vogt singled and tripled to help the A's complete their first series sweep of the Blue Jays since taking a three-game series in 2000. Oakland hadn't swept a four-game series from Toronto since May 22-24, 1981.
Steve Tolleson hit a pinch-hit home run off closer Sean Doolittle in the ninth for the Blue Jays, who have lost six straight on the road. It was his first career pinch-homer.
Toronto got a stellar outing from starter Drew Hutchison, but for the fourth straight game had little success offensively. The Blue Jays went 0 for 18 with runners in scoring position during the series.
"I thought I threw the ball well except for the two walks in the sixth," Hutchison said. "The only pitch I'd like back is the 1-2 change that went for a double."
Samardzija pitched out of a two-on, one-out jam in the first by getting Bautista to ground into an inning-ending double play. Samardzija retired 13 of the next 14 batters he faced until Jose Reyes singled with one out in the sixth.
Munenori Kawasaki followed with a double, and Melky Cabrera's groundout scored Reyes.
Hutchison (6-7) struck out four and walked two in his first career start against the A's.
NOTES: Cole Gillespie went hitless in three at-bats for Toronto after being claimed off waivers. ... Toronto OF Brad Glenn, who recorded his first major league hit on Saturday, was designated for assignment. The Blue Jays also claimed OF/DH Nolan Reimould off waivers from Baltimore. ... LHP JA Happ (7-4) takes the hill for the Blue Jays in their series opener at the Los Angeles Angels on Monday.