In a Facebook post, the state-run National Centre for Sex Education (CENESEX) blamed "new tensions in the international and regional context" for the cancellation.
Activists have condemned the move and questioned the government's motives.
Cuba was set to approve same-sex marriage under a new constitution, but removed the clause after protests.
President Miguel Díaz-Canel publicly backed the change in September, saying it was "part of eliminating any type of discrimination in society".
But the government backtracked after an outcry from religious groups.
Cuba holds events at this time every year to mark the International Day Against Homophobia on 17 May.
Why has the march been cancelled?
CENESEX posted on Facebook that it was officially cancelling the Cuban Conga against Homophobia and Transphobia "in compliance with the policy of the Party, the State and the Revolution".
The group is led by Mariela Castro, daughter of the Communist Party of Cuba's leader Raúl Castro.
No specific reasons were given for the change, with the post blaming "certain circumstances that do not help [the march's] successful development".
However, only the conga itself is cancelled, with other events going ahead as planned to mark LGBT rights.
What have activists said?
Activist Norge Espinosa Mendoza called the move "a new step backwards".
"The enemies of a more diverse and progressive Cuba will be happier now," he wrote on Facebook. "Not allowing [the parade] is a signal that... we are not welcome."
Another campaigner, Isbel Diaz Torres, told Reuters news agency the government could be "once more ceding to pressure from religious fundamentalism that has shown itself to be quite active recently".
New Facebook groups have been set up calling for people to "march for our rights".
Discrimination due to someone's sex or gender is illegal in Cuba.
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