Sales data from last week shows daily circulation consistently over 300,000, peaking at 319,000.
Johnston Press acquired the i in April, when its average audited circulation was 270,182. The firm also said that advertising revenue for the same week was the highest since the acquisition.
The company said: "These figures show a further increase from the week of the referendum, indicating a continued desire for impartial and informative journalism, highlighting the vital role that newspapers play around major milestones for the country.
"Notwithstanding the referendum, which has evidently been beneficial for newspaper groups in general, i's circulation and readership."
The online version of the newspaper, launched in April, also saw a record amount of traffic, breaking through the one million page views per week barrier for the first time.
Newspaper groups across the board have seen a spike in sales following the political and economic turmoil unleashed as a result of the Brexit vote.
Ian Whittaker, analyst at Liberum, said: "The past months have been tough for the UK newspapers as they have suffered from the UK ad spend volatility ahead of the Brexit vote.
"Yet, the Brexit vote should be positive for newspapers: in the short term, it should help boost circulation revenues given the coverage given to the Brexit vote and its consequences; and in the medium to long term, the Brexit vote - where most newspapers supported a Leave vote - will be taken as a demonstration of how much influence newspapers still have, which is a persuasive argument to use with advertisers."