Stretchable optoelectronics made of elastomeric semiconductors could enable the integration of intelligent systems with soft materials, such as those of the biological world. Organic semiconductors and photodiodes have been engineered to be elastomeric; however, for photodetector applications, it remains a challenge to identify an elastomeric bulk heterojunction (e-BHJ) photoactive layer that combines a low Young’s modulus and a high strain at break that yields organic photodiodes with low electronic noise values and high photodetector performance. Here, a blend of an elastomer, a donor-like polymer, and an acceptor-like molecule yields a skin-like e-BHJ with a Young’s modulus of a few megapascals, comparable to values of human tissues, and a high strain at break of 189%. Elastomeric organic photodiodes based on e-BHJ photoactive layers maintain low electronic noise current values in the tens of femtoamperes range and noise equivalent power values in the tens of picowatts range under at least 60% strain.