Police are investigating gambling in sports.
The footballer said officers came to his house on Thursday morning.
He was taken to the police station in Glasgow.
He has denied any wrongdoing. The subject of the questioning was not discussed by him.
Police Scotland carried out a pre- planned operation on Thursday.
Three men, aged 37, 35 and 32, were arrested on December 1 in connection with an investigation into alleged gambling incidents in sport.
The three men were not charged.
It is believed that one of the men arrested is Paul McGowan.
The club said it was aware of the police investigation.
The club will support the authorities with their inquiries and won't make any further statements at this time.
The Celtic player won seven league titles and three Scottish cups.
The forward secured his place in Scottish football folklore by scoring two free-kicks for the national team in a 2-2 draw against England.
He has been without a team for six months.
Prior to joining the club in 2014, he played for Celtic and St Mirren.
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