At least 34 people were killed in clashes between indigenous protesters and security forces in the Amazon region earlier this month.
The protesters were calling for the government to abandon plans for logging, mining and oil and gas exploration deep in the rainforest.
Opposition parties had said that Simon was ultimately responsible for the clashes, but a vote in congress earlier this week failed to generate enough votes for his removal.
Alan Garcia, the president, has also faced calls for him to stand down following the violence. He has not said who he will nominate as the new prime minister, but presidents often have a cabinet reshuffle in late July.