President Caputova will dismiss the cabinet but ask it to stay on until she at some point appoints a new one.
SaS joined a leftist opposition party in bringing the no-confidence vote, accusing the government of not helping people cope with the higher energy costs.
The political clash has prevented support for Heger's 2023 budget plan, which includes spending to offset energy prices.
Sulik told a televised briefing SaS wanted to back the creation of a new government and did not support calling early elections.
The poll-leading opposition party Hlas, though, called early elections the only option.