Armed police swooped on the multi-million pound complex after it was alleged someone had been spotted with a weapon.
A police helicopter was also brought in to sweep the area. Five women and two men, one aged 17, were later held outside the centre in East Dunbartonshire, which is used by Celtic players and staff including manager Neil Lennon who has been the target of recent parcel bombs.
The seven arrested were appearing at Glasgow Sheriff Court today in connection with the incident, which happened around 8.30pm on Sunday.
A police spokeswoman said: "Five women, one aged 19 and four, aged 21, along with two men aged 19 and 17, were arrested and are being detained in police custody in connection with an alleged firearms offence."
Celtic boss Lennon was the target of a parcel bomb sent to Lennoxtown last month.
Ten parcels intended for Celtic-related targets have now been intercepted including six hoaxes.
The latest bomb, found at a Royal Mail centre in Belfast, was posted in Scotland and addressed to Irish republican group Friends of Ireland in Glasgow.
A Celtic spokesman said: "The matter is in the hands of the police."