We measure the obscured star formation in z \sim 1 early-type galaxies . This constrains the influence of star formation on their optical/near-IR colors , which , we found , are redder than predicted by the model by Bruzual & Charlot ( 2003 ) . From deep ACS imaging we construct a sample of 95 morphologically selected early-type galaxies in the HDF-N and CDF-S with spectroscopic redshifts in the range 0.85 < z < 1.15 . We measure their 24 ~ { } \mum fluxes from the deep GOODS-MIPS imaging and derive the IR luminosities and star formation rates . The fraction of galaxies with > 2 \sigma detections ( \sim 25 ~ { } \muJy ) is 17 _ { -4 } ^ { +9 } \% . Of the 15 galaxies with significant detections at least six have an AGN . Stacking the MIPS images of the galaxies without significant detections and adding the detected galaxies without AGN we find an upper limit on the mean star formation rate ( SFR ) of 5.2 \pm 3.0 ~ { } M _ { \odot } ~ { } { yr ^ { -1 } } , and on the mean specific SFR of 4.6 \pm 2.2 \times 10 ^ { -11 } ~ { } yr ^ { -1 } . Under the assumption that the average SFR will decline at the same rate as the cosmic average , the in situ growth in stellar mass of the early-type galaxy population is less than 14 \pm 7 \% between z = 1 and the present . We show that the typically low IR luminosity and SFR imply that the effect of obscured star formation ( or AGN ) on their rest-frame optical/near-IR SEDs is negligible for \sim 90 \% of the galaxies in our sample . Hence , their optical/near-IR colors are most likely dominated by evolved stellar populations . This implies that the colors predicted by the Bruzual & Charlot ( 2003 ) model for stellar populations with ages similar to those of z \sim 1 early-type galaxies ( \sim 1 - 3 ~ { } Gyr ) are most likely too blue , and that stellar masses of evolved , high-redshift galaxies can be overestimated by up to a factor of \sim 2 .