"Starting this morning, the checkpoints are open again," the source told RIA Novosti.
According to the source, two checkpoints have been reopened – one for letting people through, the other one for transporting commercial and humanitarian cargo.
The checkpoints were closed on Sunday after Israel carried out a strike on the Gaza Strip in response to several Palestinian attacks.
Israeli authorities warned of more decisive action if attacks from the Palestinian territory persisted.
Palestinians seek to gain diplomatic recognition as an independent state on the territories of the West Bank, including East Jerusalem, which is partially occupied by Israel, and the Gaza Strip. Israel, however, has continued to erect buildings in the occupied territories.
Attempts to settle the conflict have failed so far, with the latest round of peace talks between Israel and Palestine, held in 2014, bringing no tangible results.