Four fire engines and 40 firefighters were called to the scene after smoke and flames were seen billowing from the edge of the roof at around 3.20pm.
Crews had to use special high reach appliances to douse the flames, which were extinguished by early evening.
Lend Lease will now assess fire and water damage to see whether the arena can open on time for a Rod Stewart concert in September as planned.
Welding operations are expected to come under the investigators spotlight over the next few days.
A Lend Lease spokesman said: “At first sight it appears any damage is superficial, and we have been given the go-ahead to restart work. There were no injuries. An investigation into the cause is underway.”
A Scottish Fire and Rescue Service spokesman said the fire developed in the roof space of the building, which is currently under construction.
He added: “In recognising the complexity of the structure in relation to where the fire was located the incident commander immediately requested additional special high reach appliances to attack the fire.”
SECC chief executive John Sharkey said it could be a week before it is known whether the Hydro will open in September as scheduled.