Cobb put a hand on his head after being struck. Trainers from both teams and other medical staff immediately ran onto the field.
Cobb could be seen kicking his legs while being examined on the mound. The Rays announced that Cobb remained conscious the whole time and was taken to Bayfront Medical Center in St. Petersburg for further examination.
Rays spokesman Rick Vaughn said all tests were normal and that Cobb suffered a mild concussion.
Players on both teams had hands on their heads as a stunned silence overtook Tropicana Field after the crowd gasped when Cobb was struck.
It came a month after Blue Jays starter J.A. Happ was also struck by a liner against the Rays and suffered a skull fracture.
Happ was discharged from an area hospital the following day.
The sound of the ball striking Cobb — which sounded like a bat hitting a ball — could be heard in the press box.
Rays players, manager Joe Maddon and pitching coach Jim Hickey gathered at the mound during the 11-minute delay. Shortstop Yunel Escobar was in squatting position looking down at the ground, while Hickey appeared at time at be nervously pacing near the mound.
It has been a tough week for Cobb, who left the team after starting Monday night's game against Boston due to the death of his grandmother. He was informed of the death after the game in which the 25-year old gave up a season-high six runs over four innings in a 10-8, 14-inning loss to the Red Sox.
While Happ has been fine since getting hurt, Arizona's Brandon McCarthy collapsed at a restaurant with a seizure related to the head injury he sustained while pitching last September. He was having dinner with his wife at a Phoenix restaurant when he passed out.
While pitching for Oakland last Sept. 5, McCarthy sustained what was described at the time as life-threatening injuries when he was struck in the head by a line drive off the bat of Erick Aybar of the Los Angeles Angels. He had an epidural hemorrhage, brain contusion and a skull fracture. Emergency surgery was performed that night and he was released from the hospital six days later.