Collin McHugh will start on Saturday, followed by rookie Lance McCullers on Sunday.
Straily, who is 6-6 with a 4.06 ERA at Triple-A this season, has 70 strikeouts in 77 2/3 innings. In his only season as a full-time starter, he went 10-8 with a 3.96 ERA in 2013 with Oakland, starting 27 games.
"He's got some experience to take from, he's gone down [to Fresno] and pitched very well, pitched deep into games," Hinch said. "He's earned the opportunity. We've run through a number of starting pitchers so far, some we expected, some we didn't expect, but when we acquired Dan, we expected him at some point to contribute and now is his opportunity."
Hinch expects Straily to be on the team's flight to Boston on Thursday -- an off-day for the Astros.
Marisnick starts rehab
Recovering from a strained left hamstring, outfielder Jake Marisnick was in the lineup for Fresno on Wednesday, where Hinch said he'll only play about half the game.
Hinch said the plan after that game was to have Marisnick be the designated hitter on Thursday, then let him play a full game on Friday to evaluate the hamstring.
Chandler Rome is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.