The first-known tidal disruption event (TDE) with strong evidence for a relativistic jet - based on extensive multiwavelength campaigns - is Swift J1644+5734. In order to directly measure the apparent speed of the radio jet, we performed very long baseline interferometry (VLBI) observations with the European VLBI network (EVN) at 5 GHz. Our observing strategy was to identify a very nearby and compact radio source with the real-time e-EVN, and then utilize this source as a stationary astrometry reference point in the later five deep EVN observations.With respect to the in-beam source FIRST J1644+5736, we have achieved a statistical astrometric precision about 12 μas (68 per cent confidence level) per epoch. This is one of the best phase-referencing measurements available to date. No proper motion has been detected in the Swift J1644+5734 radio ejecta. We conclude that the apparent average ejection speed between 2012.2 and 2015.2 was less than 0.3c with a confidence level of 99 per cent. This tight limit is direct observational evidence for either a very small viewing angle or a strong jet deceleration due to interactions with a dense circum-nuclear medium, in agreement with some recent theoretical studies.