Schenström's visit to a Stockholm bar with TV4 reporter Anders Pihlblad was featured in a report in tabloid Aftonbladet last Friday. The report included photos which showed her apparently kissing Pihlblad, although accusations that the pair were romantically involved have been dismissed by both Schenström and Pihlblad.
In a letter to the Prime Minister, Schenström said that she regretted "having a conversation with a journalist and drinking wine in that context."
"I have behaved inappropriately and feel that I can no longer have the necessary trust required to carry out my job. I also regret not clarifying the situation at an early stage for the Prime Minister and the general public," she said in the letter.
Fredrik Reinfeldt has not yet commented on Schenström's decision.
Earlier on Wednesday evening the State Secretary had said that she would be absent from her post for an unspecified period, a position she later revised.
In recent days, Social Democrat accusations have focused on Schenström's alcohol consumption. Pihlbad told his own channel on Wednesday that both he and she were "clearly under the influence of alcohol."
"She was absolutely not out of control, but she was clearly affected," he said.
Leading opposition politicians have asked whether she was on call for the country's crisis management apparatus - questions Reinfeldt has refused to answer.
Reinfeldt has stood by Schenström, who is viewed as the most important member of his personal staff and who served as his press secretary prior to him becoming prime minister. Earlier on Wednesday he said he had continued confidence in his aide.
"She is a long-serving colleague and I have learnt that I can trust her word that she was capable of taking decisions," he told SVT. But opposition spokesman Håkan Juholt said that she had shown "poor judgment."
"There is no room in that job for less than 100 percent confidence in her judgment," he said.