An MRI scan has shown the Paraguay frontman has tendinitis, and as a result he has pulled out of his country's World Cup qualifiers against Peru and Uruguay.
The 26-year-old has a history of knee problems but he believes proper rest and recuperation will enable him to return to the Rovers team next month.
"I've been forcing the injury in the last few weeks, playing with injections," said Santa Cruz in the Lancashire Evening Telegraph.
"I've reached a point where I had to decide if I should continue but run the risk of having to stop for two or three months, or if I should stop now and see if the injury gets better.
"I'm sad not to be there (with the national team).
"I don't like having to make a decision like this, but in the long term it means that I should be ready for games in November."