Microstructure emission, involving short timescale, often quasi-periodic, intensity fluctuations in subpulse emission, is well known in normal period pulsars. In this Letter, we present the first detections of quasi-periodic microstructure emission from millisecond pulsars (MSPs), from Giant Metrewave Radio Telescope observations of two MSPs at 325 and 610 MHz. Similar to the characteristics of microstructure observed in normal period pulsars, we find that these features are often highly polarized and exhibit quasi-periodic behavior on top of broader subpulse emission, with periods of the order of a few μs. By measuring their widths and periodicities from single pulse intensity profiles and their autocorrelation functions, we extend the microstructure timescale-rotation period relationship by more than an order of magnitude down to rotation periods ∼5 ms, and find it to be consistent with the relationship derived earlier for normal pulsars. The similarity of behavior is remarkable, given the significantly different physical properties of MSPs and normal period pulsars, and rules out several previous speculations about the possible different characteristics of microstructure in MSP radio emission. We discuss the possible reasons for the non-detection of these features in previous high time resolution MSP studies along with the physical implications of our results, both in terms of a geometric beam sweeping model and temporal modulation model for micropulse production.