The Serb world number four accepted a late wildcard into the ATP 250 grasscourt event, desperate to fine-tune his erratic form, but managed just one game against Canadian qualifier Vasek Pospisil before the rain set in.
While fans sought cover and raised umbrellas, organisers pushed back the resumption of play several times before finally accepting the British summer weather had got the better of them at around 6pm local time.
The tournament director brought Wednesday's start of play half an hour earlier to 10.30am, with a backlog building.
As well as Djokovic, women's French Open champion Jelena Ostapenko and runner-up Simona Halep are scheduled to play, but in Ostapenko's case only if British hope Johanna Konta can complete an earlier round earlier in the day.
Other big names hoping to stretch their limbs on the lush lawns of Devonshire Park include women's world number one Angelique Kerber, and French players Richard Gasquet and Gael Monfils.
The forecast is not great, though, with rain predicted for much of the morning, and lengthy spells of the afternoon.
Fans who left Devonshire Park seeing barely a ball struck will at least be refunded, the tournament said.
(Editing by: Toby Davis)
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