The trio includes Roberto Di Matteo (Italy), Filippo Rossi (Switzerland) and Jesus Medina (Venezuela). Rossi had previously been misidentified as Italian.
Critics say Venezuelan prisons are overpopulated and inmates are malnourished, despite government plans to reduce inmate populations.
"The Swiss Embassy in Caracas is in contact with the appropriate authorities and is assisting this Swiss national in accordance with the consular protections afforded him," the Swiss foreign ministry said.
The Italian foreign ministry said its mission "has been following from the very beginning the arrest of Italian national Roberto Di Matteo, and is in close contact with local authorities".
Di Matteo, Rossi and Medina were arrested Friday after entering Tocoron prison in northern Aragua state with a television crew, according to the rights group Foro Penal.
"They were... part of a media investigation when they were arrested," the national journalists union said.
Media rights groups did not confirm for which outlets the Italian and Swiss journalists were reporting. Medina is a photojournalist for anti-government website DolarToday.
The union released a photograph of the three journalists taken from the back, apparently handcuffed and escorted by two military personnel. Their cellphones and small cameras were confiscated.
Union representatives told AFP they saw the journalists were in good health late Saturday.
"They are doing well and show no signs of mistreatment," according to the SNTP union.
"They had an invitation to enter Tocoron. They had registered to enter when they were barred access and then arrested. It seems there was a counter-order to bar them access."
The journalists were first stopped by prison officials before being handed to the authorities, according to the union.
Foro Penal director Alfredo Romero said some of his group's lawyers had traveled to provide legal aid to the trio, who are being held by national police.
Late last year, rights group Una Ventana a La Libertad estimated that there are some 88,000 inmates across a country with an official prison capacity of 35,000.
President Nicolas Maduro's government, which says it is being unfairly disparaged in national and international media, says it has successfully applied measures to pacify prisons and raise their standards to international norms.