Emmanuel Mugabe from the national Parents Association of Uganda told AFP the tower's rainbow colours were "satanic" and signalled an "invasion of homosexuality through manipulation of children's minds".
"We are happy the rainbow painting has been removed before we removed it ourselves," he said.
A local group had painted one of the park towers in Entebbe in rainbow colors as part of an effort to refurbish the site, the town's mayor Fabrice Brad Rulinda said in a statement released on Wednesday.
"For years, the children of Uganda have only understood the rainbow as a beautiful arch of colors and biblically it reflects the beauty and majesty of God," Rulinda said.
"It is unfortunate that certain movements have decided to use the rainbow to represent and reflect certain acts that go against the norms of the people of Uganda," he added.
"We need to curb any vices that would corrupt the minds of our children and it is on this background that the concerns raised by the public were heeded to and the rainbow painting was removed from the children's park."
The incident follows an uproar in southwestern Uganda where local authorities in Kasese are allegedly trying to pass legislation recognizing the rights of gay, lesbian and transgender people.
In an address to parliament on Wednesday, Uganda's state minister for local government, Victoria Busingye, advised authorities "to drop the proposed by-law since it was contradicting the laws of Uganda and the social, cultural wellbeing of the people of Kasese and Uganda at large".
Uganda's government last month set up a committee to investigate the alleged "promotion" of gay, lesbian and transgender rights in schools.
Uganda has strict anti-gay legislation but there have been no prosecutions for consensual same-sex acts in the country in recent years.
In 2014, a Ugandan court struck down a bill passed by MPs and signed by President Yoweri Museveni that sought to impose life imprisonment for homosexual relations.