UEFA said Basel had been charged with "inadequate organisation" of the game at home to Schalke 04 after four Greenpeace protesters wearing orange boiler suits descended on ropes which they had dropped from the roof and unfurled a huge banner.
The banner read "Gazprom, don't foul the Arctic" and "Free the Arctic 30".
The protesters then hauled themselves back on to the roof while officials watched from the touchline and the match continued.
It was not clear how the protesters got on to the roof of the stadium which is owned by the club and also contains a shopping centre and retirement flats.
Russian authorities detained 30 members of the pressure group who were aboard icebreaker the Arctic Sunrise when they broke up attempts to scale state-run Gazprom's Prirazlomnaya offshore oil platform on Sept. 18.
The 30 activists, protesting about oil-drilling in the Arctic, have been remanded in custody for two months.
Greenpeace said in a statement after Tuesday's protest that it had shown a "red card" to Gazprom, which sponsors both the Champions League and Schalke 04.
UEFA said that it had also opened a separate case after Schalke fans used pyrotechnics immediately before the kick-off.