She also told abusers: “You will not get away with your crimes.”
It comes after police warned the new rules made victims more vulnerable.
Campaigners also warn that domestic abuse has already increased elsewhere in the world as more people at risk from abuse are forced to stay indoors with their abusers due to the pandemic.
“I am acutely aware that the necessary guidelines about social distancing and self-isolation may leave the victims of hidden crime, such as domestic abuse and child sexual abuse, feeling especially isolated, vulnerable and exposed,” said Ms Patel, in her newspaper column.
“But my message to every potential victim is simple: we have not forgotten you and we will not let you down.
“And my message to every perpetrator is equally as simple: you will not get away with your crimes.”
She said the government would protect victims, saying it has given £1.6bn to local councils to help those in need and was working with charities.
The National Domestic Abuse Helpline was also continuing to operate, she said.
“Whilst our advice is to stay at home, anyone who is at risk of, or experiencing, domestic abuse, is still able to leave and seek refuge. Refuges remain open, and the police will provide support to all individuals who are being abused – whether physically, emotionally, or otherwise,” she added.
Under the government’s new measures, everyone has been told to stay at home and only leave the house for four reasons: shopping for basic necessities, exercise, any medical need and travelling to work if you cannot work from home.
But the “unprecedented” measures could lead to more people finding themselves being victims of domestic abuse, Leicestershire Police warned earlier this week.
The force said health concerns and job losses may also add pressure, causing some people to experience abuse for the first time.
And the charity Refuge said staff were “working round the clock” to make sure its services remained open.
It issued some tips to people who are at risk, including keeping your mobile phone charged and with you and, if a partner becomes violent, try to avoid the kitchen, garage or anywhere that might have potential weapons.
Ms Patel also said that because schools were closed, “millions of children are spending more time online than they otherwise would have and may be even more vulnerable to online predators”.
She said the government was working with charities, schools and law enforcement to ensure parents and children know how to stay safe online.
“This country has a huge heart, and this government will not allow anyone to be forgotten, particularly those most in need of our support,” she added.
Ms Patel’s comments come days after the Duchess of Cornwall urged women who are isolating at home with an abusive partner to seek advice and support from the National Domestic Abuse Helpline.
Southall Black Sisters, a non-profit organisation that campaigns on gender-related violence, and the cross-party organisation Compassion In Politics have written to hotel chains urging them to give unoccupied hotel rooms to abuse victims.
Rights activists in China say there have been increasing instances of domestic violence there, while support services in Australia reported an increase in coronavirus-related family abuse because of the pandemic.