The former Aam Aadmi Party leader said the Truecaller app -- which reveals callers' identity -- showed that the number belongs to "Dawood".
Damania tweeted that she received the call at 12.33 am, asking her to withdraw all cases against Khadse, from a number prefixed with +92 -- the country code for Pakistan.
The app flashed "Dawood 2" on the screen, she said in the tweet and posted screenshots to back her claims.
"The caller told me in his own words ...Tune jina haram kar rakha hai sabka... Teri family hai na... Tera jina Haram kar dunga (You have made everyone's life miserable....You have a family...I will make your life miserable)," she told a press conference.
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"I don't know who the caller was and whether the call was routed or not... or it was a direct call. So it's up to the government to investigate the matter and clear the air."
Damania also demanded the government should protect whistle blowers like herself who are exposing the misdeeds of corrupt people by putting own life at risk.
The activist lodged a complaint with the Vakola police station in suburban Santacruz about the phone call. Police officials from Vakola later visited her home and recorded her statement, she said.
Speaking to PTI, Damania said the caller spoke rudely with her and threatened to make her life difficult.
"I immediately spoke to Chief Minister Devendra Fadnavis and he was prompt to assure me that the Joint Commissioner of Police (Crime) will look into the matter," she added.
Damania alleged the police are taking its "casually" and did not deem it necessary to post a policeman outsider her home.
The activist, through tweets, also appealed to Prime Minister Narendra Modi and Home Minister Rajnath Singh for taking action.
Based on Damania's complaint, an FIR has been lodged under IPC sections 506 (punishment for criminal intimidation) and 507 (criminal intimidation by an anonymous communication), a police official said.
"This investigation must be handed over to agencies like, RAW or IB as this number is said to belong to Dawood Ibrahim," party spokesperson Preeti Sharma Menon said.
Damania is among the petitioners who have filed a PIL in the Bombay High Court seeking action against Khadse for alleged graft.