The family of Mohsen al-Daeri has been unable to contact him since he left Aden for Riyadh early on Wednesday, the source said, requesting anonymity to discuss sensitive matters.
He had boarded the same plane as a delegation of the UAE-backed Southern Transitional Council delegation of more than 50 people including top members.
The STC says they have been "arbitrarily detained" and that they have not been able to contact them.
The minister is not an official member of the STC, but he hails from Dhale, the home province of the group's leader Aidarous al-Zubaidi.
STC forces seized control of much of the south last month, ousting Saudi-backed rivals and angering Riyadh.
On Thursday, Yemen's presidential body dismissed Daeri from his position.
Daeri stayed in Aden during the STC land grab, which was later reversed by Saudi military power aided by their Yemeni allies on the ground.
The offensive exposed a rift between Gulf allies Saudi Arabia and the United Arab Emirates, which back rival factions of the Yemeni government.
The Saudi-led coalition has accused Zubaidi of fleeing to the United Arab Emirates capital Abu Dhabi after failing to join the top-level delegation that went to Riyadh.
Zubaidi pulled out of the trip after learning that Saudi Arabia would ask him to dissolve the STC, an official from the group had told AFP earlier this week.
On Friday, the delegation announced the STC's dissolution from Riyadh, a decision dismissed as made under duress by their colleagues based in the UAE.
Saudi Arabia and the UAE support different factions in Yemen's internationally recognised government, which runs the country's south backed by a patchwork of militias with shifting allegiances.
Yemen's government was forced out of the capital, Sanaa, in 2014 by Iran-backed Houthi rebels who continue to control the more populous north.
The Houthi takeover prompted a military intervention by the Saudi-led coalition, including the UAE, to back the government. The ensuing civil war caused hundreds of thousands of deaths and a major humanitarian crisis.
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