Reyes was lifted after his first at-bat because of a tight left hamstring, an injury that first bothered him late in spring training. The star shortstop led off the game and was robbed of a hit on a diving catch by Rays centre fielder Desmond Jennings.
"I tried to run a little bit faster between home plate and first base, and I kind of feel my hammy there," Reyes said. "So I have to slowdown and get out of the game because I don't want to get any worse."
Reyes missed several games during the final week of spring training and wasn't at 100 per cent for exhibition games Friday and Saturday in Montreal.
"Irritated the same spot, so that's a concern," Toronto manager John Gibbons said.
Several hours later the Blue Jays put him on the DL.
Reyes said the hamstring was "good enough" to play in Montreal and felt better Monday.
"When I tried for a little speed, something not right," Reyes said.
Reyes missed 66 games last season after going on the DL April 13 with a sprained left ankle -- after just 10 into his first season with the Blue Jays.
Price (1-0) allowed two runs and six hits over 7 1-3 innings to beat R.A. Dickey in a matchup of 2012 Cy Young Award winners. The hard-throwing lefty walked one and struck out six before a crowd of 31,042 at Tropicana Field -- the Rays' ninth consecutive sellout for a home opener.
"It's really disappointing and frustrating," Dickey said. "You feel like you let a lot of people down. Against David Price, one of the best pitchers in baseball, if you don't match him inning per inning, it's going to be tough to win the game. I put us in a hole early. Walked some guys early, gave up some 0-2 hits with runners in scoring position, and that was the game."
Dickey dropped to 14-13 with a 4.21 ERA last season after winning 20 games and NL Cy Young honours with the Mets two years ago. The 39-year-old knuckleballer is off to another shaky start after allowing six runs, five hits and walking six over five innings against essentially the same Tampa Bay lineup he went 3-1 against in 2013.
Joyce had a sacrifice fly and two-run double off Dickey (0-1), who yielded six two-out runs in five innings. Evan Longoria got the Rays going with a first-inning RBI single and Wil Myers drove in two more when he singled with the bases loaded in the second.
Price limited the Blue Jays to four singles and had only allowed two runners past second base before Maicer Izturis opened the eighth with his second hit of the day. Pinch-hitter Erik Kratz followed with a first-pitch, two-run homer over the centre field wall.
The 28-year-old lefty became the Rays' first 20-game winner and edged Justin Verlander in AL Cy Young balloting two years ago. He got off to a slow start in 2013, but finished strong after spending more than a month on the disabled list, leading the majors in innings, complete games and fewest walks per nine innings after July 2.
NOTES: The Rays haven't lost a home series to the Blue Jays since April 2007. ... Blue Jays closer Casey Janssen, who's on the 15-day disabled list due to a strain in his left abdominal area and lower back, doesn't feel the injury will be a long-term problem. ... The four-game series continues Tuesday night with RHP Alex Cobb getting the start for Tampa Bay and the Blue Jays countering with RHP Drew Hutchison.