Toronto said Tulowitzki will be monitored for the next week before the Blue Jays determine a timetable for his return. The Blue Jays said he will speak about the injury Sunday.
"We'll probably have a little better idea in a few days how long,'' Blue Jays manager John Gibbons said.
Tulowitzki backpedaled into short center to catch Didi Gregorius' popup with two outs. After Tulowitzki caught the ball, he was hit from behind by Pillar.
Tulowitzki at first held the ball and transferred it to his right hand as he collided with Pillar, then seemed to be stunned and fell to the field as the ball rolled out of his hand. Tulowitzki was attended to by a trainer and walked off on his own Saturday, although with a limp.
"I don't think he anticipated me coming,'' Pillar said. "I couldn't feel any worse about it. It's probably the worst thing I've ever experienced on the field.''
After saying X-rays of his rib and chest were negative, the Blue Jays said he would have an MRI. During the nightcap, Toronto said he sustained a small crack to his scapula and upper back muscle bruising.
The Blue Jays went on to sweep the doubleheader and extend their AL East lead over the Yankees to 4 games.
Tulowitzki, 30, has a history of injuries that have limited him to an average of just 88 games per year over the previous three seasons. In 125 games this season with the Colorado Rockies and the Blue Jays, Tulowitzki is batting .279 with 17 homers and 70 RBIs.
The five-time All-Star was acquired just before the July trade deadline in a deal that sent shortstop Jose Reyes and three prospects to the Rockies.
Right-hander Marcus Stroman wondered whether Tulowitzki will play again this year.
"I'm sure he's got it in his head that he's going to do everything in his power to make it back,'' the pitcher said. "I know that even if he's not back, he'll be with us in spirit and he'll be cheering us on.''
Information from ESPNNewYork.com's Andrew Marchand and The Associated Press was used in this report.
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