"Adam Szalai's PCR test was positive, so the team captain cannot be at the disposal of the technical staff against Albania and Andorra," said the MLSZ in a Twitter post.
Hungary, who last qualified for the World Cup in 1986, play Albania away on Sunday and Andorra in Budapest next week.
"Adam Szalai was immediately isolated and will soon leave Telki (national team training base)," it said.
The 33-year-old Szalai, who has scored 24 times in 74 appearances for Hungary, captained the side in their 4-0 loss to England in Budapest on Thursday.
Hungary lie third in World Cup qualifying Group I behind England and Poland.