Screen grabs showing the website with messages from gay activists are being circulated on social media sites.
Homosexual acts are illegal in Uganda and gay people have faced physical attacks and social rejection.
Earlier this year, a controversial anti-gay bill, which proposes to increase the penalties for homosexual acts from 14 years in jail to life, was re-tabled in the Ugandan parliament.
The bill was first introduced in 2009 but never debated - and the MP backing the legislation says a clause proposing the death penalty will be dropped.
It originally said those found guilty of "aggravated homosexuality" - defined as when one of the participants is a minor, HIV-positive, disabled or a "serial offender" - would face the death penalty.
The Uganda Justice Law and Order Sector website was also reportedly taken over by hackers this week.
Ambrose Ruyooka, commissioner for the Information Communications Technology ministry, told the BBC the problem had now been rectified.
The government has created a directorate of security for all government websites and tightened cyber laws to counter rising cyber crime, he said.
An activist named @DramaSett3r on Twitter is said to be behind the attacks.