Thunberg retweeted the above post from 350.org, which suggested Credit Suisse provided US$57 billion to companies looking for new fossil fuel deposits, and asked Federer to "wake up now".
The hashtag #RogerWakeUpNow began trending on Twitter soon after.
Federer responded to the activists before the Australian Open, saying he is open to "innovative solutions" to climate change and discussing "important issues" with Credit Suisse.
"I take the impacts and threat of climate change very seriously, particularly as my family and I arrive in Australia amid devastation from the bush fire," Federer said in a statement to Reuters.
However, before his record-breaking exhibition match against Rafael Nadal in South Africa, the Swiss star addressed the controversy once again.
Speaking to Swiss publication Tages Anzeiger, Federer suggested his popularity was being exploited, and has chosen to overlook the criticism.
"I am sometimes misused for certain purposes," Federer said.
"When I help one person, I am criticised for not doing it with others. I have reached a point where I have to think carefully about what I am doing.
"But I also have to be able to overlook criticism. I can't be everywhere, I can't do everything. I am also a father and tennis player.
"I am aware that I can make a difference, take the microphone and address certain things. But I can't do that all the time."
Federer also believes "attacking others" is not the correct approach when addressing climate change.
"It is important that you choose the right things at the right time and get your message across in a fair way. Not by attacking others," he said.
"I know I can make a difference with my popularity. For others, for the planet, for the animals. And I think it's good what has recently been raised about collective consciousness."
Federer is currently at No. 3 on the ATP rankings, and lost his Australian Open semi-final to eventual victor Novak Djokovic.
