The Serie A side are set to be without their striker for three weeks after he suffered a muscle strain against Sampdoria on Wednesday
The Argentine picked up the injury during the side's 2-0 victory over Sampdoria, and the 31-year-old will now be monitored to determine the extent of the strain.
"We have yet to see if the stretch is of first or second degree," Inter doctor Piero Volpi told SkySport24.
"In the first case he will be out for 20 days, in the second about 40 [days]. But with a little luck he could take the field against Roma [on April 17], and maybe heal in eight to 10 days."
However, a statement on the club website later added that the strain would likely require longer period of rehabilitation.
"Tests were carried out on the attacker Rodrigo Palacio which showed a lesion miotendinea second degree on his left hamstring," it stated.
"Recovery times from the injury will be evaluated in the coming days."