The one-page letter addressed to him was received by Mumbai Police Control Room on July 25 through post, Maria told PTI here today.
"We will take revenge for Gaza. In 1993, you (Maria) got a chance. This time you won't. Stop us if you can," reads the letter signed simply as "Mujahideen".
The other contents of the letter, written in Hindi as well as English, hinted a terror attack in the city, he said.
"We are verifying the authenticity of the letter. However, we are not taking the threat lightly. The Crime Branch and all the police stations have been alerted," Maria said.
The Mumbai police chief had recently issued an internal circular to the police department which has reference to terror attacks at various places in the past, including Maharashtra, during the "festival season" and asked the personnel to be alert.
Following the Friday's terror threat, police is leaving no stone unturned to ensure a tight security across the city on the eve of Eid, he said.
Maria, presently accorded Z-category security, had investigated the 1993 Mumbai serial blasts as Deputy Commissioner of Police (DCP), rounding up many members of the Dawood Ibrahim gang and other members of his family.
Since last year, NIA, Delhi Police and Maharashtra Police have arrested some key Indian Mujahideen operatives, including Yasin Bhatkal.
The Israeli military offencive on Gaza has claimed the lives of scores of Palestinians and left thousands of others wounded.