Cato Pedder, from Haslemere, Surrey, suffered shrapnel wounds to her leg and a fractured ankle in the incident on Friday night.
A spokesman for the British High Commission in Kampala said that Ms Pedder had been sitting with friends outside the hostel in Lungujja, a few miles from the city.
"It seems that someone managed to enter the compound and threw an explosive device towards them," he said.
"She was injured, as were two other tourists, a South African and an Australian.
"She was taken to hospital and has now been transferred to a private hospital, the Kololo.
"As far as we know the police have not made any arrests yet, but there are strong indications that the attacker was not specifically targeting tourists."
The spokesman said High Commission officials had visited Ms Pedder, who was travelling around the country, in hospital three times.
"She seems in good spirits and her injuries are not too serious. We have arranged for her to speak to her mother and she will be flying out here later in the week."
A spokeswoman for the Kololo Hospital said Ms Pedder was in a comfortable condition, but would be undergoing surgery later today.
Several people died earlier this year in Kampala in a spate of grenade attacks directed mainly at police units.Reuse content