The Regimental Blues, who have been at the centre of several high-profile controversies in their short life, will march on the morning of March 16 instead of the afternoon, when Aberdeen and Inverness supporters will flock to Celtic Park.
The group had originally proposed to march from the vicinity of Celtic Park in the east end of the city to George Square and back at midday and ending near 3pm in the Bridgeton area.
But the council has had the parade moved to a 9.30am start to avoid clashing with the Aberdeen and Inverness fans heading to Celtic Park or arriving at Queen Street station.
Around 100 people are scheduled to take part in the parade by the Regimental Blues, which describes itself as a "pressure Group standing for the Protestant Loyalist Community of Scotland".
A council source said: "The concern was more why they were staging something on St Patrick's weekend than clashes with Aberdeen fans who dislike Rangers.
"There wasn't much resistance from the Regimental Blues to the move. "
The Regimental Blues have had parades moved in the recent past. Last September it was ordered to re-route an event after organisers said they wanted to march through a section of Glasgow's east end "to put a burning stick into the nest".
A Glasgow City Council spokesman said: "Officers have negotiated with the organisers to agree a earlier start time, which will minimise conflict with football traffic."