The wedding took place in Assam on June 27 and a small reception was organised here a week later.
Two out of the 41 attendees have tested positive for COVID-19, they said.
The deputy commissioners of East Khasi Hill and Ri- Bhoi districts have initiated the inquiries.
At least 41 persons had attended the wedding held at a resort in Guwahati, despite the Meghalaya governments decision to restrict citizens from travelling to Assam, which has witnessed a sharp increase in coronavirus cases, Deputy Chief Minister Prestone Tynsong said.
Preliminary investigation said that the 41 persons had not registered themselves at the entry point at Byrnihat in Ri-Bhoi district while returning from Assam on June 28.
"We have asked the deputy commissioners to conduct inquiries into the lapses that led to the incident," Tynsong told .
Based on the report, the government will take appropriate action, he said.
"The 39 persons have been quarantined. After a few days, RT-PCR tests will be conducted on them again," the deputy chief minister said.
Meanwhile, Chief Minister Conrad K Sangma on Wednesday said that four more persons have tested coronavirus positive in the state capital, including 3 BSF personnel and a person from Tripura who had come here for treatment at the NEIGRIHMS hospital.
As many as 25 BSF personnel who returned to the state have contracted the disease.
Since the detection of the first patient in the state on April 13, a total of 99 COVID-19 cases have been registered in the state.
Two persons have succumbed to the disease so far, and 43 patients have recovered.
There are 54 active cases now. JOP MM MM