The MHA's move came after Goa Chief Minister Pramod Sawant wrote to Union Home Minister Amit Shah requesting a probe by the Central Bureau of Investigation.
Shah visited Lalbaugcha Raja, a prominent Ganesh pandal, on Monday during his two-day visit to the city.
As many as 151 police personnel, including 28 women officers, from across the country were selected for the prestigious award.
Officials said overstaying in India beyond the visa date can lead to fine, an imprisonment of up to five years and even a ban on entering the country again.
Union Home Ministry has amended certain rules related to the Foreign Contribution (Regulation) Act (FCRA) allowing Indians to receive up to Rs 10 lakh in a year as opposed to Rs 1 lakh earlier.
The home department is waiting for the Chief Minister's final approval over the complaint.
The Punjab Police also registered an FIR dated January 6 in Ferozepur's Kulgari police station against nearly 150 unidentified protesters who blocked Modi's cavalcade.
The Centre's move comes days after it, on December 25, refused to renew the FCRA license of Mother Teresa's Missionaries of Charity.
Organisations such as the Missionaries of Charity will not be eligible for the extension benefits as their applications for a renewal of the FCRA registration have already been rejected.
The MHA said that if any case has been booked in states and the UTs under Section 66A of the IT Act, 2000, they should be immediately withdrawn.