SAMHD1 was previously characterized as a dNTPase that protects cells from viral infections. Mutations in SAMHD1 are implicated in cancer development and in a severe congenital inflammatory disease known as Aicardi-Goutieres syndrome. The mechanism by which SAMHD1 protects against cancer and chronic inflammation is unknown. Here we show that SAMHD1 promotes degradation of nascent DNA at stalled replication forks in human cell lines by stimulating the exonuclease activity of MRE11. This function activates the ATR-CHK1 checkpoint and allows the forks to restart replication. In SAMHD1-depleted cells, single-stranded DNA fragments are released from stalled forks and accumulate in the cytosol, where they activate the cGAS-STING pathway to induce expression of pro-inflammatory type I interferons. SAMHD1 is thus an important player in the replication stress response, which prevents chronic inflammation by limiting the release of single-stranded DNA from stalled replication forks.