The boy's small coffin was laid out in the cathedral of his hometown of Nola near Naples ahead of the funeral.
Several thousand mourners attended, many of them parents with young children holding white flowers.
Italian Prime Minister Giorgia Meloni took part in the service, which filled the church to capacity.
The town of about 35,000 people had declared an official day of mourning and most shops remained closed.
Hundreds of posters with the boy's photograph were displayed in the streets and in the square in front of the cathedral.
Domenico's case has gripped Italy for months.
The toddler, who was born with a severe heart defect, received a donor heart in late December.
However, the organ never functioned because it had been incorrectly cooled during transport.
The child died on February 21 in the intensive care unit of a hospital in Naples.
Prosecutors are now investigating several doctors and paramedics - both in Naples, where the transplant was carried out, and in the northern city of Bolzano, where the heart had been removed from a deceased boy.
During transport, the organ was not cooled with conventional ice as is standard practice but came into contact with much colder dry ice, effectively freezing it.
Despite this, doctors in Naples decided to proceed with the transplant.
According to Italian media reports, attempts were even made to thaw the frozen organ using hot water.
Domenico was then kept alive by machine for almost two months, which also caused severe damage to other organs.
Eventually, there was no longer any hope of saving him.
The doctor responsible for the operation in Naples has since been suspended from his duties.
In an interview earlier this week he described himself as a "victim," triggering fresh outrage.
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