Police said the wall caved in during rain and thunder showers that hit the city yesterday.
Human Singh Rajpurohit (30) died on the spot, while brother Tug Singh (28) succumbed to his injures during treatment, police said, adding they were residents of Satauni village in Barmer district.
The victims' bodies were handed over to their family members after post-mortem, they said.
A case has been registered and the matter is being investigated, police added.