How appendages, such as plant leaves or animal limbs, develop asymmetric shapes remains a fundamental question in biology. Although ongoing research has revealed the genetic regulation of organ pattern formation, how gene activity ultimately directs organ shape remains unclear. Here, we show that leaf dorsoventral (adaxial-abaxial) polarity signals lead to mechanical heterogeneity of the cell wall, related to the methyl-esterification of cell-wall pectins in tomato and Arabidopsis. Numerical simulations predicate that mechanical heterogeneity is sufficient to produce the asymmetry seen in planar leaves. Experimental tests that alter pectin methyl-esterification, and therefore cell wall mechanical properties, support this model and lead to polar changes in gene expression, suggesting the existence of a feedback mechanism for mechanical signals in morphogenesis. Thus, mechanical heterogeneity within tissue may underlie organ shape asymmetry.