Edwin Chiloba’s body was found on Wednesday on a road in Uasin Gishu County, in the west of the country.
Officers said the motive for the killing was not yet known. However, human rights organisations in Kenya have linked the killing to Mr Chiloba’s sexuality.
LGBT people face severe discrimination in the highly-conservative country, and same-sex relationships are punishable with jail sentences.
Police said a motorcycle taxi operator reported seeing the box being dumped by a vehicle with no licence plates.
It was reported to police at a nearby roadblock who opened the box and found his body inside.
The deceased was identified as Chiloba and his body was taken to the Moi Teaching and Referral Hospital to establish the cause of death.
Police spokesperson Resila Onyango said: “We don’t know for now why he was killed that way. Experts are handling the matter”.
“Words cannot even explain how we as a community are feeling right now. Another soul lost due to hate. You will be missed,” said rights organisation Galck.
The National Gay and Lesbian Human Rights Commission paid tribute to him as a “loved and valued” member of the LGBT community who used his platform to fight for human rights.
“The murder itself was terrible, but the callous way his body was discarded makes the situation all the more mortifying,” it said.
“Edwin’s death reminds us that queer bodies continue to be under attack all over the country.”
Last year, the killing of non-binary lesbian Sheila Lumumba led to a social media campaign to get #JusticeForSheila.