People living close to the venues have complained about concert-goers leaving cars outside their homes.
The city council is planning to introduce permit holder only parking in a number of streets in the area between 6pm and 10pm, seven days a week.
The roads affected will be Corunna and Minerva Street, Minerva Way, St Vincent Crescent and West Greenhill Place.
At present, permits are only needed from Monday to Friday between 8am and 6pm.
A council spokesman said: "This experimental order has been introduced to address the concerns of the local community regarding parking difficulties."
Local councillor Philip Braat said the area has suffered parking problems in the past but the situation has recently got worse.
He added: "The Hydro is a fantastic venue for the city but we need to make sure there is a balance between the needs of the city and the needs of local residents."
Mr Braat said the new parking restrictions should be in place by the end of this month or start of March and will initially run for 18 months.
"This gives us time to monitor the situation and see if there is any need for amendments later on.
"The problems may not be resolved overnight but by putting these proposals in place there should hopefully be an improvement."
Green councillor Nina Baker said she had received complaints about parking long before the Hydro opened.
She added: "The problem is this is not an area capable of absorbing any more parking, so with 12,000 people going to the Hydro it was bound to make things worse."
A new 1600-space multi-storey car park was built to coincide with the opening of the venue last year.
But Ms Baker said many motorists are opting to park in local streets rather than wait in a queue to get in and out of the car park.
And she claimed the situation was not helped by having major events in more than one of the three venues on the SECC site on the same night.
The Anderston/City councillor said: "If people are arriving by car it suggests they don't live nearby and arrive without any knowledge of local restrictions.
"They see the queue for the car park and decide they will take a chance and park a 10-minute walk away from the venue.
"I don't know if these new parking restrictions will be the answer unless there is real high-profile enforcement.
"Restrictions are only as good as the effort you are willing to make in enforcing them."