They also face an agonizing wait to see if the boy has also contracted HIV, Il Messaggero reported.
The child was pricked by the needle, discarded by a drug addict, while playing in Europa park, on Via Venezia in the northern Italian city in June.
But results of tests for Hepatitis B take up to six months, while an HIV test is repeated three months after potential exposure.
"We are desperate,” his father was quoted in Il Messaggero as saying.
"But it’s not over; my son has to repeat the HIV tests. I am now looking for a lawyer to sue the council."