Former world number one Hewitt, a four-time champion at the pre-Wimbledon warm-up event, was scheduled to face 10th seed Dimitrov in the third match on the main show-court in west London.
But a series of showers meant the first match on the court, sixth seed Sam Querrey's encounter with Aljaz Bendene, was yet to finish by 1500GMT.
Querrey, a surprise winner of Queen's in 2010, or Bendene will play Hewitt or Dimitrov in the last 16.
The Querrey-Bendene tie was into the final set when the latest downpour arrived, but there was still former US Open champion Juan Martin del Potro's match against Xavier Malisse to be played before Hewitt could take the court.
In one of the few matches to beat the rain, Czech 12th seed Lukas Rosol, who famously shocked Rafael Nadal at Wimbledon last year, advanced to the second round with a 6-7 (7/9), 6-3, 6-2 win over Australian qualifier Samuel Groth.