The yellow parachute had the words “KICK OUT OIL” and “GREENPEACE” emblazoned on it.
Footage circulated on social media showed the parachutist colliding with cables supporting an overhead camera before appearing to lose control.
UK broadcaster ITV, which televised the match, showed the protester eventually landing on the field and escorted off the pitch by security.
ITV also showed minor debris from the incident almost hitting France coach Didier Deschamps.
Greenpeace Germany tweeted an apology, in part saying “due to a technical fault, a forced emergency landing was endangered and one person was apparently injured as a result. We hope everyone is fine. #FRAGER.”
CNN has reached out to Greenpeace for further comment. Munich police did not immediately respond to CNN’s request for comment.
On its website, Greenpeace says the organization aims to “defend the natural world and work for a green and peaceful future.”
UEFA in its statement added: “UEFA and its partners are fully committed to a sustainable EURO 2020 tournament and many initiatives have been implemented to offset carbon emissions.”
The match was not impacted by the incident. France won the Group F match 1-0.