Rasmus aggravated the injury during an eighth inning at-bat of Friday night's 10-4 loss to the Yankees. He originally suffered the ailment during the club's recent West Coast trip and is now expected to miss at least a couple of games.
"He's getting some further tests this morning just to determine how much he reaggravated the groin," manager John Farrell said. "After the game last night, our feeling was that he was going [to miss] two to three days as he did coming out of the game in Oakland.
"We don't think the initial tests in the training room last night were more severe than on the West Coast trip."
Rasmus was forced to miss two games in the Oakland series because of lingering soreness and he'll likely experience a similar fate this time around.
Despite the setback, Farrell remains optimistic that Rasmus will be able to avoid a stint on the disabled list and could return as early as Monday against the White Sox.
"Based on the tests last night, no," Farrell said of a possible DL move. "If we can get through it by keeping it to two or three days down, we'd much rather prefer that than 15."
Toronto can ill afford to lose Rasmus from its lineup for any period of time. The Blue Jays are already trying to make do without the services of regulars Jose Bautista, Brett Lawrie, J.P. Arencibia and Adam Lind.