Woltemade put the visitors in front with a header after 31 minutes, scoring his first goal in Germany colours. The win kept Germany top of their group on goal difference ahead of Slovakia, who beat Luxembourg 2-0.
Both Germany and Slovakia have three wins in four matches, with only the first-placed side guaranteed to qualify for next year's World Cup. The Germans host Slovakia in Leipzig in November.
Despite the loss, Northern Ireland are only three points off the lead. Their final two fixtures are away against Slovakia and at home to Luxembourg, who have lost four from four.
Looking to qualify for a World Cup for the first time since 1986, Northern Ireland came into the match with wind in their sails after a shock 2-0 win over the previously unbeaten Slovakia.
Germany coach Julian Nagelsmann also wanted to keep the momentum from Friday's 4-0 win over Luxembourg.