Støre was speaking to broadcaster NRK in the wake of the controversy surrounding ousted former deputy leader Trond Giske, who recently left his position with the party after a series of accusations of inappropriate conduct towards female colleagues were levelled at him.
Some of the accusations were connected to social events such as parties for Labour members.
The full details of the accusations have not been made public.
But the scandal is a major embarrassment for the Labour party, which prides itself on being at the forefront of equality issues, and which recorded disappointing results at the last legislative elections in October.
In December, Giske apologised for his previous behaviour and appeared to suggest that alcohol had been a factor in it.
“I think I must accept that I have not been thoughtful enough about my behaviour and role. That can mean when there are differences in seniority or age or in social situations with a lot of alcohol,” he said on NRK's Dagsrevyen programme on December 21st.
“We are going to have a new policy on alcohol,” Støre said to NRK on Thursday.
“I am not going to concern myself with whether or not people drink, but we are not going to be paying for it,” the party leader continued.
Free drinks, including alcohol, have previously been the norm at party events, writes NRK.
The new policy will come into effect at the Labour national leadership conference at the end of this month, Støre confirmed.
Earlier this week, Kristian Tonning Rise, the leader of the Conservative party's youth wing, announced that he would be leaving that post, citing that he had not acted in a manner befitting his position in social situations. Inappropriate behaviour at events involving alcohol was also cited in that case.
“Alcohol is the elephant in the room. It erases boundaries and leads to people doing things they shouldn't,” Støre said to NRK.
The Giske scandal comes as the issue of rape and sexual harassment moves to the fore in Norway in the wake of the downfall of US movie mogul Harvey Weinstein.
In November, a thousand artists denounced rape, assault and harassment in manifestos published by the Norwegian media.