The incident occurred on Saturday when Gambhir had gone for a walk in Rohini with her mother, they added.
The accused snatched the phone from her on the pretext of asking for directions, the police said.
Since it was evening, she could not note down the vehicle's registration number, they said.
In her complaint, the diplomat said that the accused asked her for directions to Hanuman Mandir. When she started pointing towards the temple while holding her phone, they snatched the phone and fled, the police said.
Gambhir stated that the iPhone had a US-registered SIM card and some important files related to her work, they said.
In September this year, exercising India's right to reply after Pakistan Prime Minister Shahid Khaqan Abbasi raked up the Kashmir issue at the UN General Assembly, Gambhir had made a strong rebuttal by calling Pakistan a "terroristan".
Ukrainian Ambassador Igor Polikha's mobile phone was snatched in September while he was taking pictures of the Red Fort, following which one person was arrested.
Delhi Police has registered as many as 7,870 cases of snatching this year till November 30.