Lowrie, who sprained his right thumb diving into second base during a pickoff attempt Wednesday, didn't feel as good as the team would have hoped after fielding ground balls and playing catch on Friday.
"He wasn't able to grip the ball as well as we'd like," Mills said. "We're going to wait and see how that works out. It's pretty tender."
Mills raised some doubt whether Lowrie would be able to play in any of next week's exhibition games -- Monday at Double-A Corpus Christi and Tuesday and Wednesday against the White Sox in Houston. An X-ray and an MRI showed no structural damage to the thumb.
"Jed was going so well and swinging the bat so well," Mills said. "We're going to have to check him out and make sure he's healthy, throwing and swinging the bat and everything else. It's going to be interesting to see how he comes around."
When asked if Lowrie might not be ready for Opening Day, Mills said: "There's always that concern, there's no doubt. But these next couple of days are going to be crucial in trying to figure out how it is and ... as we get into those exhibition games, whether he's going to be able to play at all."
Lowrie, who is hitting .333 with two homers and seven RBIs in 36 at-bats, and had a .429 on-base percentage this spring, fielded ground balls with one hand Saturday and swung the bat with his left hand.
"I'm not ready to put the bat in the right hand yet," he said.
Lowrie isn't ready to handicap his Opening Day availability.
"It's a day-to-day thing, and it's basically what my hand will let me do," he said. "Right now, it's still too sore to pick up a bat."
Astros general manager Jeff Luhnow said the team is prepared for the worst, but hoping for the best.
"It's really about how much [Lowrie] can tolerate and how quickly he feels ready to get back into games," he said. "That could be a few days; it could be a couple of weeks, and anywhere in between. We need to proceed with contingency plans in place for Jed being ready to go Opening Day, and Jed not being ready to go Opening Day.
"The good news is even if he's not ready to go Opening Day, we're not talking about an extended absence. We're talking about something relatively short. It would be nice to have him in there on Opening Day, and he's a big part of the team this year, but if he's not it won't be the end of the world."
If Lowrie starts the year on the disabled list, it could be backdated to March 28, assuming he doesn't play in any games the rest of the spring. That means if Lowrie started the season on the DL, he would miss the first six games of the regular season.
As far as contingency plans, the Astros still have Rule 5 shortstop Marwin Gonzalez in camp and have brought Brian Bixler and Angel Sanchez back over from Minor League camp.