The man, who has been identified as Pateh Sabally, a Gambian in his early 20's, died after jumping from a bridge into the waterway on Sunday.
Police said they were treating the death as a suicide, but have opened an investigation after shocking video footage showing passersby shouting racist abuse at the dying man was shared around the world. Public prosecutors are reviewing footage from four mobile phones and CCTV in the area.
One video, first posted by local newspaper Il Gazzettino, showed tourists looking on from the waterside as Sabally drowned.
Some onlookers yelled abusive comments including "Go on, go back home" and "let him die".
Others called for a passing boat to throw life buoys to Sabally - the boat reversed to reach the man and threw two buoys, but he made no attempt to grab hold of them. Divers later retrieved his body from the canal.
On Friday, a local priest organized a memorial event for Sabally, while Venice mayor Luigi Brugnaro announced that city authorities would cover the costs of his funeral. The money will come from Brugnaro's personal cost of living allowance in "a gesture of respect from Venice towards Pateh Sabally and his shattered dreams," he said.
"The death of this young man has saddened all of us, and we feel pity towards those who, faced with the adversities of life, no longer find the strength to react to desperation," added Brugnaro.
Sabally, who was aged either 21 or 22 (his birth month is not known), had reportedly arrived to Sicily by boat from Gambia, but his application for asylum was denied.
Brugnaro warned against politicizing the man's death, describing it as "an act of personal desperation" and criticizing those who used the tragedy to stir up controversy or for "profiteering".
Addressing "do-gooders", Brugnaro said: "We can't continue to nurture the hopes of half the world of coming to Italy. Everyone needs to realize it is impossible for our country to continue managing such a large-scale phenomenon in the way it has done so far."
"We need to understand the future implications of this; above all the tragedies and suffering of [migrants and refugees]," he added.