Walker struck his seventh goal of the season before firing in an in-swinging corner that led to Paddy McLaughlin doubling York's lead in the 3-0 win over Burton.
"He started to feel really weak and ill during the first half so he came off at half-time but we're hoping it's not anything too bad," said Mills.
"We've not scored too many from corners and we've always known Jason's quality from dead-ball situations.
"We see it in training all the time and I first thought about him taking them a couple of weeks ago. We felt the time was right and he put an unbelievable ball in for the second goal."