The first quake hit Jodhpur at 1521 hrs, while the second quake hit Pithoragarh in Uttarakhand at 1832 hrs, it said.
However, there were no immediate reports of loss of life and property.
Earlier in the day, a strong quake jolted Tibet, tremors of which were felt in the northeastern state of Arunachal Pradesh, the IMD said.
The Himalayan belt is known for high seismological activity.