The Chancellor wrote in the caption that he was "excited to see the memes".
To deflect any possible worries about his health, Mr Scholz also wrote: "Thanks for the well wishes, it looks worse than it is!"
Mr Scholz fell while jogging on Saturday and sustained bruises to his face, prompting him to cancel some appointments this weekend, the government said.
His spokesperson told reporters in Berlin later on Monday that the Chancellor was doing well considering the circumstances.
"He was in quite a good mood this morning, but still looks a bit battered," Steffen Hebestreit said, adding that the photo, apparently taken at the chancellery, was published "so that everyone can get used to how he will look in the next week or two".
Some social media users jokingly connected the injuries to rows within the governing coalition, while the internet site of the city of Cologne, which hosts a large annual carnival, suggested that revellers could come next year dressed as “Pirate Olaf”.
On Sunday, the 65-year-old German leader cancelled appointments in the central Hesse region, where a state election is being held on October 8. However, he was expected to attend public appearances later on Monday in Berlin.
Local media reported that Scholz fell while running in his hometown of Potsdam which is located 17 miles south-west of the German capital.
Mr Scholz has led Germany since December 2021. He previously served as the country's finance and labour minister, and as mayor of Hamburg.
In a profile on his party's website, Mr Scholz says that he hated sports when he was at school but acquired a taste for it from his wife, Britta Ernst.
"Today I jog as often as I can," he says.
Mr Scholz says he tries to find time for jogging, rowing or walking two or three times a week and also enjoys cycling.