"It will not be proper to reject the ED application and it is allowed," said judge J C Jagdale.
The agency can interrogate Indrani Mukerjea tomorrow and on December 6.
In May, the ED registered the case under the Prevention of Money Laundering Act against Karti Chidambaram, INX Media and its directors Peter and Indrani Mukerjea, and others.
It sought the Mumbai court's permission to question Indrani Mukerjea, as she is in judicial custody in the Sheena Bora murder case.
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The Foreign Investment Promotion Board (FIPB) permitted INX Media to receive FDI for Rs 46.2 million, however, it received foreign investment totalling to Rs 3,053.6 million during August 2007 to May 2008, the ED said.
"Thus excess foreign exchange equivalent to Rs 3004.4 million beyond the disclosed and permitted foreign investment was received by INX media from three Mauritius-based foreign investors," the agency said.
It is suspected that illicit funds generated by Peter and Indrani Mukerjea have been siphoned off to overseas unknown destinations and routed back in the UK and India through Mauritius-based foreign investors, the ED said.
"Rabin... Peter and Indrani have laundered money and are involved in financial transactions in UK connected with illicit funds generated in India," the application said.
The ED also noted that the murder of Sheena Bora, Indrani Mukerjea's daughter from earlier relationship, was suspected to be motivated by financial reasons.
The CBI had earlier filed an FIR against Karti Chidambaram and the Mukerjeas.
It was alleged that Karti Chidambaram had received money from INX Media for using his influence to manipulate a tax probe against it in a case of violation of Foreign Investment Promotion Board conditions to receive investment from Mauritius.
Sheena Bora's murder came to light in August 2015 after Mukerjeas' driver Shyamvar Rai, arrested in another case, spilled the beans.