Dominguez, 22, was acquired from the Marlins with left-hander Rob Rasmussen, who is going to Double-A Corpus Christi.
Astros manager Brad Mills indicated Johnson would play first base for the four games until the All-Star break, but wouldn't commit to anything beyond that. He was also asked if Brett Wallace was in the team's plans at first, but was non-committal.
"We've got four games now before the All-Star break and we're going to go this route for these four games and make some adjustments and see where we're at and let guys get at-bats in those positions and then we can go from there," Mills said.
Matt Downs and Scott Moore could also get some time at third. Johnson played a lot of first base in Spring Training and handled the position adequately. He has played only two innings at first base this year.
"I played some games over there this season and got a bunch of starts in Spring Training," he said. "It's a knockdown position. I'm fairly comfortable over there, so it's not something I'm worried about."