The city's Public Processions Committee ordered the prohibition of the parades - due to take place at the weekend - on Wednesday.
Recent weeks have seen "unacceptable" disorder breaking out in connection with a number of marches and counter-protests.
A Glasgow City Council spokeswoman said: "The council has always been clear that the law expects it to facilitate public processions; including those that some people oppose or find offensive.
"However, the right to march has to be balanced against the rights of people and communities across Glasgow."
She added: "It is clear, both from the intelligence gathered by police and the tone of comments made by supporters and protestors, that tensions are high and the situation threatens to deteriorate further.
"The council directly appeals to those who would have taken part in these marches, or who planned to mount protests against them, to comply with the orders made and not bring further disruption to city streets."
On Saturday, a policeman was injured after he was hit by a pyrotechnic thrown by a protester, while 11 people were arrested as two marches through the streets of Glasgow descended into violence.
Just over a week earlier, Police Scotland had to step in a deal with "significant disorder" at a march in Govan.
There had been 14 marches planned during the rest of September - including 11 believed to involve republican or loyalist groups.
The banned parades on Saturday are Bridgeton Protestant Boys Flute Band, Pride of the North Flute Band, Republican Network for Unity as well as two from the Whiteinch Orange and Purple District No 7.
Partick Orange and Purple District 15 had been planning to march on Sunday.
Justice Minister Humza Yousaf tweeted: "Pleased that Glasgow City Council have made this decision -we will continue our dialogue with GCC to find a longer term solution to reduce the number of loyalist/republican parades going through Glasgow. I know the citizens of Glasgow have frankly had enough."
Chief Superintendent Hazel Hendren, Divisional Commander for Greater Glasgow Division, said: "The decision to amend the route or the timing, or to prohibit any procession, is a matter for the relevant local authority.
"Police Scotland is required to assist councils to make informed decisions by making appropriate representations on notifications which could potentially significantly risk public safety, disorder, damage to property or disruption to the life of the community."