The Danish Refugee Appeals Board (Flygtningenævnet) on Monday morning said it would review the woman's case, a process her lawyer Jytte Lindgaard said would take at least three months.
Lindgaard declined to comment on the decision.
“But I can say generally that the risk that something happens to her is much too great,” she told Denmark's Ritzau news agency. “She has among other things given lectures on what it is like to be a lesbian asylum seeker.”
Denmark's decision last month to deny asylum to three Ugandan lesbians was harshly criticised by the campaign group LGBT Asylum, which fights for the rights of gays, lesbians and transsexual people within the Danish asylum system.
“We are very relieved!” the organisation posted on Facebook on Saturday. “But we can not relax completely. First, we must now work to ensure that she actually does receive asylum when her case be re-examined, and secondly there are still two rejected people in Ellebæk jail awaiting deportation.”
Asylum campaigners from the group Welcome to Denmark mounted a demonstration on Monday at Copenhagen Airport in support of the woman, with more than 20 protestors linking arms in front of the check-in at Terminal 2.
Being gay or lesbian has been illegal in Uganda since 1952, when the colonial government brought in a series of anti-gay laws.
In 2013, Uganda's parliament debated a controversial law that made homosexual acts punishable by death, although by the time it was enacted the penalty had been softened to life imprisonment.
The law was annulled by the country's Constitutional Court in August 2014, but gay Ugandans still face long prison sentences if caught by the police.
Hanne Gyberg from LGBT Asylum told Ritzau last month that this was far from the worst risk faced by homosexual men and women in the country.
“Homosexuals risk persecution from other civilians, their families and clan members as well as blackmail and assault,” she said. “Homosexuals cannot expect police protection if they are attacked, threatened or killed.”