Johansson, who is the state secretary of Minister of Culture and Sport Stefan Wallin, said he would leave his post on Thursday.
The Swedish-language newspaper Hufvudstadsbladet reports the Johansson acted inappropriately at a recent event held at Sweden's embassy. Eyewitnesses charged him with groping women's breasts, among other things.
A working committee from Wallin's Swedish People's Party reviewed the matter on Thursday.
The Ministry of Education said Johansson has apologised for his actions.
"I deeply regret that my lack of judgement, caused by alcohol and drowsiness, led to behaviour that I myself cannot condone. I am sorry for what happened and I have received an important lesson that will follow me throughout my life," he said.
Hufvudstadsbladet,