Italy's epicentre of the global outbreak admitted it was experiencing a "constant and progressive increase of the deceased awaiting cremation".
A statement from the city council said the waiting time at the Crematorio di Lambrate had reached 20 days.
Any longer could cause "hygiene-sanitary problems", the city council said on its website.
The thriving northern powerhouse of just under 1.4 million -- a global capital of fashion that serves as Italy's main financial hub -- has been under lockdown since February.
Its Lombardy region recorded the first COVID-19 death in Europe on February 21.
It has now registered 7,960 of Italy's 13.915 official coronavirus fatalities.
"To help families in this difficult moment, starting Friday, it will be possible to bury loved ones at no cost," the city said in the statement.
It did not disclose how many bodies were awaiting cremation.
But it noted that the number of people who died over the course of the past month had nearly doubled to 2,155 from the 1,224 who passed away in March last year.
"Even in Milan, we are witnessing a rise in deaths," Milan's civil services councillor Roberto Cocco said.
"Our funeral and cemetery employees are working tirelessly and with a high degree of responsibility."
Bergamo, northeast of Milan and at the heart of the Italian outbreak, received a steady shipment of new coffins throughout March to deal with the dead.
Its was eventually forced to send out dozens of bodies a week for cremation to neighbouring towns.
"The large number of victims has meant that Bergamo's crematorium could not cope on its own," mayor Giorgio Gori said in a statement to AFP last Thursday.
The number of official COVID-19 fatalities across Italy has more than doubled in the past week.