Catalyzes the condensation of formaldehyde and glutathione to S-hydroxymethylglutathione. S-(hydroxymethyl)glutathione = formaldehyde + glutathione Binds 2 Zn(2+) ions per subunit. One-carbon metabolism; formaldehyde degradation; formate from formaldehyde (glutathione route): step 1/3. Belongs to the Gfa family.