Baroness Beverley Hughes, Greater Manchester's deputy mayor for policing and crime, said authorities were preparing for serious incidents after the government announced a three-week lockdown.
After a meeting of the region's COVID-19 emergency committee, Baroness Hughes said: "I think we are beginning to see a rise in domestic abuse incidents.
"We anticipated this might happen in the very stressful circumstances for many families."
She later said the overall level of domestic abuse cases was as expected, but that officers were classifying incidents believed to have a connection to the virus.
Baroness Hughes added that families were being asked to stay at home and that many had significantly less money, or no income, after tougher measures were put in place.
She said: "The potential for tension to arise in the home as a result of what we are asking people to cope with, in order to suppress the virus, is going to increase and therefore we would be right to think this might display itself in an increase in the number of domestic incidents we are called to.
"We are preparing for that.
"Some of those most serious incidents will be challenging to deal with, particularly if the victim needs to be moved to a refuge, but the police specialise in these kind of cases and the local partners, local authorities, they're working together really closely to prepare for that."
Baroness Hughes said there had also been a small rise in the number of hate crimes.
On Tuesday, Justice Secretary Robert Buckland told the Commons Justice Committee that the UK may see more cases of domestic abuse, as well as online crime and fraud during the pandemic.
Avon and Somerset Police has reported a 20.9% increase in domestic abuse incidents in the last two weeks - from 718 to 868.
In Cumbria, officers have asked postal workers and delivery drivers to look out for signs of abuse.
Detective Chief Inspector Dan St Quintin is urging people to "look out for each other as much as possible" in the coming weeks and months.
He added: "We would also like to extend this plea to those such as postal workers, delivery drivers, food delivery companies and carers who will still be visiting houses, to keep an eye out for any signs of abuse and to report any concerns to us."
He said the Bright Sky app, which can be disguised for those worried about partners checking their phones, provides support and information for victims.
The National Centre for Domestic Violence says it "fully supports" the plea, as it warned of "huge dangers lurking for victims", as the whole country "grapples with the consequences of COVID-19".