Gotze has been struggling to secure regular first-team action at Bayern this campaign, partially due to injury, making just 12 appearances in all competitions for the Bundesliga leaders in 2015-16.
He recently resumed regular training after overcoming a hamstring problem, but has featured just once since re-joining his team-mates at Bayern.
"We are counting on Mario for the European Championship," Low said at a news conference ahead of the friendly against England.
"He is a very important player for us. I know what he is capable of.
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"His attitude is great and he is part of our plans.
"Mario has some incredible technical skills. He is very refined and can decide matches."
Low left Gotze's Bayern team-mate Joshua Kimmich out of his squad for the friendlies against England and Italy, but he revealed the 21-year-old is still in contention for a place in his Euro 2016 squad.
"Our planning for the Euros is underway. I have a number of young players from the Under-21 squad on my list," he added.
"Kimmich has already shown what he can do in a number of positions. I see a future for him in a central role, either in central midfield or at centre-back.
"There is a lot of competition for places. Some of our youngsters are pushing hard for a place in the squad."