Elucidating the role of molecular stochasticity in cellular growth is important to understanding phenotypic heterogeneity and the stability of cellular proliferation. We used time-lapse microscopy to measure fluctuations in the instantaneous growth rate of single cells of Escherichia coli and in the expression of metabolic enzymes. We show that expression fluctuations of catabolically active enzymes can propagate and cause growth fluctuations. Conversely, growth fluctuations propagate back to perturb expression. Homeostasis is promoted by a noise-cancelling mechanism that exploits fluctuations in the dilution of proteins by cell-volume expansion. Thus, molecular noise is propagated not only by regulatory proteins but also by metabolic reactions. The results suggest that cellular metabolism is inherently stochastic, and a generic source of phenotypic heterogeneity.