Quantum mechanics allows the existence of "virtual states" that have no classical analogue. Such virtual states defy direct observation through strong measurement, which would destroy the volatile virtual state. Here we show how a virtual state of an interacting many-body system can be detected employing a weak measurement protocol with postselection. We employ this protocol for the measurement of the time it takes an electron to tunnel through a virtual state of a quantum dot (cotunneling). Contrary to classical intuition, this cotunneling time is independent of the strength of the dot-lead coupling and may deviate from that predicted by time-energy uncertainty relation. Our approach, amenable to experimental verification, may elucidate an important facet of quantum mechanics which hitherto was not accessible by direct measurements.