Bolt, who is scheduled to run the 100m at the Golden Spike IAAF World Challenge in Ostrava, Czech Republic on Friday, travelled to Germany after posting 10.05 seconds in his season opener and had treatment there, said Mills.
Bolt is targeting an unprecedented Olympic threepeat at the Rio de Janeiro Games in August where he will be defending his 100, 200 and 4x100 relay titles.
"I think he has a slight discomfort in his hamstring, so he didn't bother push it after that, but he'll be alright," Mills told Jamaican radio station Hitz 92fm. "He's in Germany as we speak and the doctors say he will be fine."
Bolt, the 100 and 200 world record holder, got off to a moderate start in his season-opening race before stepping away from the field in the last 60 metres and cruising to the tape.
He later told reporters he was a bit rusty but would be ready for Jamaica's Olympic trials from June 30 to July 3 in Kingston.
"If you saw the race, you could see he was grimacing a bit," said Mills, who has guided Bolt to six gold medals at the last two Olympics. "(I) didn't think he was under any pressure, but he was just grimacing because he wanted to really push it, but he was just grimacing that he couldn't get the chance to do so."