Ms Gonzalez, 36, whose career has mainly focused on environmental issues, is due to take part in Sunday’s presidential debate in the capital.
Mr Villavicencio, 59, a former journalist and member of the country’s national assembly, was shot three times in the head as he left a public event in the capital on Wednesday.
His death has shocked a nation that has largely escaped the decades of drug-gang violence, cartel wars and corruption that has blighted many of its neighbours.
Mr Villavicencio’s campaign focused on corruption and gangs, and was one of only a few candidates to allege links between organised crime and government officials in Ecuador.
Interior Minister Juan Zapata said on Thursday that six suspects had been arrested, adding that were Colombians who were members of organised criminal groups,
Patricia Villavicencio, his sister, said “this crime can’t go unpunished… We are hurting, with a broken soul, there is no justice, there is no protection”.