Rachael Maskell, the MP for York Central, has called on the city council to reverse its decision to stop all funeral services.
Ms Maskell said the City of York Council's decision was "a step too far" and could be a breach of the UN Declaration of Human Rights.
The council announced that from Thursday 9 April it was no longer holding any funerals at York Crematorium.
It added: "These have been very difficult and sad decisions for us to make, but necessary in light of public health concerns."
Ms Maskell said she had been contacted by many distraught families in York and that she had raised her concerns with the government.
She said: "This is a very difficult time for everyone, but when crowds are still in our supermarkets and working in warehouses across the city, to stop close family members being able to say goodbye to a child, a parent or partner is completely insensitive and deeply damaging."
Funerals provide an important role in the grieving process, and to be denied such an opportunity will cause lasting pain for families.
She added: "At this time some people are unable to be with close family members as they die, and then not being able to be with them at their funeral is a step too far.
"Constituents have shared their heartache over this decision by the council. a council who could institute safe funeral distancing measures as other councils are, like North Yorkshire, which are enabling funerals to go ahead with ten family members while observing safe social distancing, as set out in the government guidance.
"York must immediately revert to this too."
An online petition started by a woman who said it "was a decision of which directly impacts my auntie, along with many others grieving for their loved ones" has been signed by more than 1,000 people.
The City of York Council said it was a difficult decision but said there could be up to 14 services a day, meaning 150 people could visit the crematorium in one day.
Sharon Stoltz, director of public health for City of York Council, said the Council's "utmost priority" was to protect people.
She said: "I understand how difficult this decision will be for many people and the pain it may add to the loss of a loved one, and my heart goes out to anyone who is affected by it.
"Our utmost priority is that we protect people from the spread of Coronavirus where it is possible to do so and to ensure that the health of those we work with, the public, council staff, funeral directors and other partners are protected.
"Since the decision was announced, we have had further discussions with funeral directors and faith leaders and agreed with them that we will allow one celebrant or minister to perform a short service that will be filmed free of charge.
"We hope this will provide some comfort to those who are affected during these difficult times."
A Local Government Association spokesman said: "Councils are continuing to hold funerals in accordance with the latest government guidance and are making specific arrangements on a local basis to ensure that social distancing can be maintained.
"We are seeking further guidance on funeral services from central government."