Police Scotland carried out an operation in Bothwell, South Lanarkshire, Bonnyrigg in Midlothian and Airdrie in North Lanarkshire on Thursday.
The force said that three men were arrested and released without charge pending further inquiries.
A Police Scotland spokesman said: “Following a pre-planned police operation on Thursday December 1, three men aged 37, 35 and 32 were arrested in the Bothwell, Bonnyrigg and Airdrie areas in connection with an investigation into alleged gambling incidents in sport.
“All three men were released without charge pending further inquiries.”
Griffiths, 32, confirmed he spoke to police but said he was not arrested and denied any wrongdoing, the BBC reported.
The footballer scored 13 goals in 31 appearances for Wolves before moving on to Celtic, where he netted 123 goals in 261 appearances.
The former Livingston and Hibernian forward won the last of his 22 Scotland caps in November 2020.