Yarmouk, once home to hundreds of thousands of Palestinian refugees and Syrian nationals, is one of several districts on the edge of the Syrian capital which the army has surrounded to choke off rebel forces seeking Mr Assad's overthrow.
Amnesty said in a report: "The Syrian government has committed numerous war crimes as part of the siege of Yarmouk.
"Hundreds of civilian residents of Yarmouk have been killed, wounded or have perished as a result of deliberate starvation and destruction of their means of support, direct attacks on civilians and indiscriminate attacks."
Mainly Sunni Muslim rebels in northern Syria have also besieged two Shi'ite towns, but most of the blockades across the country have been carried out by Mr Assad's forces. Only around 20,000 residents remain in Yarmouk.