That could take at least a couple days.
"We can't stress how important he is to our club," Scioscia added, "so we have to err on the side of caution with him."
Aybar, who has started each of the Angels' first 48 games at shortstop, felt his hamstring grab on him while executing a squeeze bunt in the bottom of the fifth and jogged gingerly back to the dugout, prompting him to get replaced by Taylor Featherston in the top of the sixth.
The 31-year-old switch-hitter was batting .344 since May 3 and had settled into the Angels' leadoff spot.
If Aybar ultimately has to miss an extended period, the Angels could probably call up Josh Rutledge or Ryan Jackson from Triple-A Salt Lake. One of them would share the position with Featherston, though Grant Green could also get some starts at shortstop, and Johnny Giavotella could be a candidate to bat leadoff.
"This guy's as important as you want to talk about on our team," Scioscia said of Aybar, who's expected to, at the very least, miss Friday's game.
Alden Gonzalez is a reporter for MLB.com. Read his blog, Gonzo and "The Show", follow him on Twitter @Alden_Gonzalez and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.