Red Pepper’s list appeared under the headline: “Exposed”, raising concerns of a witch-hunt against gay people.
Western governments have condemned Mr Museveni’s decision to approve the bill.
Uganda is a deeply conservative society where most people oppose homosexuality.
Homosexual acts were already illegal in Uganda, but the new law bans the promotion of homosexuality and covers lesbians for the first time.
In 2011, Ugandan gay activist David Kato was killed in what rights activists said was a homophobic attack.
His name had appeared on a list published by the now-defunct Ugandan Rolling Stone magazine, calling for the execution of gay people.