Amnesty said President Museveni "must urgently veto this appalling legislation", adding that it would "institutionalize discrimination, hatred, and prejudice" against the LGBTQ community.
The discussion about the bill in parliament has been laced with homophobic language and Museveni himself last week referred to gay people as "these deviants."
Ugandan lawmakers hastily passed the bill on Tuesday evening ordering harsh penalties for anyone who engages in same-sex activity.
Homosexuality is already illegal in the conservative East African nation and it was not immediately clear what new penalties had been agreed.
"This ambiguous, vaguely worded law even criminalizes those who 'promote' homosexuality," Amnesty's east and southern Africa director, Tigere Chagutah, said.
Lawmakers amended significant portions of the original draft legislation with all but one speaking in favor of the bill.
MP Fox Odoi-Oywelowo, a member of Museveni's National Resistance Movement, party who spoke against the bill, told AFP that offenders would face life imprisonment or even the death penalty for "aggravated" offences.
Despite the bill's passage in parliament, the 78-year-old Museveni has consistently signaled he does not view the issue as a priority, and would prefer to maintain good relations with Western donors and investors.
US Secretary of State Antony Blinken on Wednesday urged Uganda to reconsider implementation of an anti-gay bill that outlines harsh penalties for same-sex activity.
"The Anti-Homosexuality Act passed by the Ugandan Parliament yesterday would undermine fundamental human rights of all Ugandans and could reverse gains in the fight against HIV/AIDS," Blinken wrote on Twitter.
"We urge the Ugandan Government to strongly reconsider the implementation of this legislation."
Uganda is notorious for its intolerance of homosexuality - which was criminalized under colonial-era laws.
But since independence from Britain in 1962 there has never been a conviction for consensual same-sex activity.
In 2014, Ugandan lawmakers passed a bill that called for life in prison for people caught having gay sex.
A court later struck down the law on a technicality, but it had already sparked international condemnation, with some Western nations freezing or redirecting millions of dollars of government aid in response.
Last week, police said they had arrested six men for "practicing homosexuality" in the southern lakeside town of Jinja.
Another six men were arrested on the same charge on Sunday, according to police.
