Blalock went 2-for-4 with a double in five innings at first base in an afternoon game at the team's complex in Surprise, Ariz., manager Ron Washington reported.
Out since April 26 because of a partially torn left hamstring, Blalock is expected to rejoin the Rangers for this weekend's series at Cleveland.
Blalock was scratched from Double-A Frisco's lineup on Thursday when his hamstring tightened up, but Washington said he had no problems on Monday.
Blalock has volunteered to move from third base to first, to accommodate Ramon Vazquez, who brought a team-best .333 batting average into Monday's game at Minnesota.
That means less time at first base for Frank Catalanotto, who spoke with Washington about the subject.
"We're going to try to get him at-bats as best we can. I was just honest with him. Cat's a class act," Washington said.
Washington also plans to begin increasing Milton Bradley's time in the outfield and decrease his time as the DH, keeping him in the lineup as much as possible.