Hennrich became a member of the Bundestag in the 2002 German federal election, always being directly elected in the Nürtingen constituency[2] He was a member of the Health Committee,[3] where he served as his parliamentary group's rapporteur on pharmaceutical supply.
Hennrich became a member of the German delegation to the Parliamentary Assembly of the Council of Europe (PACE) since 2010. In the Assembly, he served on the Committee on Culture, Science, Education and Media (2014–2018; since 2022); the Sub-Committee on the Cultural Heritage (2010–2012); the Sub-Committee on Development Issues (2010–2012).[4]
In July 2022, Hennrich announced that he would resign from active politics by early 2023 and instead become managing director of the German Medicines Manufacturers´ Association (BAH).[5]