Dveri group, which was formed in 1999 as a Christian right-wing youth organisation before becoming a political party in 2015, claimed Ana Brnabic was suggested because of Western pressure.
The party with close ties to the Serbian Orthodox Church said: "Is it possible that the ruling majority has no other candidate for the prime minister-designate but the one imposed by the West, which dictates all the moves by this government?"
President Aleksandar Vucic described selecting her as "a difficult decision reached in the interest of Serbia and its citizens". He had previously claimed he would not approve anyone for the post who does not have at least two children.
The appointment of Brnabic - who is currently the minister for public administration and local government - has also infuriated Pro-Russian nationalists.
President Vucic was prime minister before his election as president in April and was expected to appoint a loyalist to replace him as he moved into the largely ceremonial presidential position. Although Brnabic is not a member of the ruling Serbian party, she is considered loyal to the President.
The former extremist-turned-reformist President has promised to boost gay rights in an effort to move Serbia closer to European Union membership.