The announcement on the handover of the islands, which have been under Egypt's protectorate, sparked demonstrations last week.
Hamdeen Sabahi, the leader of the Egyptian Popular Current, submitted a 10-page complaint to an administrative court in Cairo over the case, calling for the deal to be suspended immediately.
The document claims the Tiran and Sanafir islands are "part of Egypt's sovereign control" and cannot be relinquished without a referendum. It also says the surrender of the two islands threatens Arab and Egyptian national security and also endangers Egypt's relations with Saudi Arabia.
Tiran, the larger of the two islands and closer to Egypt's southern Sinai coast, is in the minds of many older Egyptians associated with their country's four wars against Israel, between 1948 and 1973, a time of nationalistic fervor and patriotism. More recently, Tiran has become a popular destination for tourists.
Sabahi was a member of parliament during ousted autocrat Hosni Mubarak's years in office. He ran against el-Sissi in 2014 as the sole alternate candidate but was crushed in a landslide victory for the former military chief.