Parnpree, who doubles as deputy prime minister, will be accompanied by armed forces chief General Songwit Noonpakdee.
The foreign minister said arrangements to transport the released Thais back to Thailand on a chartered flight may take two or three days.
Another 15 Thai workers are still being held by Hamas, but the militant group said it would release more hostages during its ongoing truce with the Israeli Defence Forces, he added.
The truce is due to end early on Tuesday morning.
On Friday, 10 Thai nationals were among the first batch of hostages released by Hamas.
Another four Thais were released on Saturday and three more on Sunday, making a total of 17.
Prime Minister Srettha Thavisin thanked his Malaysian counterpart Anwar Ibrahim for playing a role in securing the release of the Thai workers.
Srettha was speaking to reporters at Don Mueang military airport before flying to Hat Yai for a meeting with the Malaysian PM at the Sadao border checkpoint.
Srettha said he would seek Anwar’s help in ongoing talks with Hamas for the release of all Thai hostages.
Border trade with Malaysia would also be on the agenda, he added.
Srettha said the pair would also discuss Malaysia’s latest proposal for ending violence in the insurgency-hit southern border provinces, as well as cooperation at border checkpoints.