Opposition supporters accused Mr Sargsyan, who was made prime minister last week after serving 10 years as president, of clinging to power.
"The street movement is against my tenure. I am fulfilling your demand," Mr Sargsyan said in a statement.
Former prime minister Karen Karapetyan has taken over as acting PM.
President Armen Sarkissian accepted Mr Sargsyan's and the government's resignation.(BBC news)