Justice Minister Ashraf Rifi said he was denying the request because Hannibal Gaddafi was a wanted man in Lebanon.
The businessman son was charged on Monday with withholding information about the disappearance of Lebanese Shiite cleric Mussa Sadr.
Sadr went missing in 1978 during an official visit to Libya, along with an aide and a journalist.
Gaddafi was kidnapped on Friday in Lebanon's Bekaa valley near the Syrian border in mysterious circumstances.
He was freed by police hours later and taken in for questioning, security sources said.
But a decades-old judicial agreement between Syria and Lebanon did not apply to Kadhafi, who was wanted by Beirut and therefore should not have been granted refugee status in Syria, he said.
It is unknown how long Kadhafi had been in Syria.
The lavish lifestyles of the Kadhafi family and entourage helped fuel the anger in Libya that sparked the protests that led eventually to the strongman's ouster and killing in 2011.
That year, as the dictator was battling the uprising against him, a private jet carrying Hannibal Gaddafi's Lebanese wife Aline Skaf was refused permission to land at Beirut airport.
Two other sons of the late dictator, Saadi and one-time heir apparent Seif al-Islam, are in detention in Libya.
Three more were killed during the Libyan revolt.
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