The weather had deteriorated long before the scheduled 7.15pm start and umpires Peter Hartley and Neil Mallender had little option but to call off the keenly-anticipated local derby around one hour later.
With no play possible, the large crowd were denied the opportunity of seeing Andre Russell make his Notts debut.
The West Indian all-rounder has joined the county on a short-term contract and will be available for just four matches, although the remainder will all be played away from Trent Bridge.
The abandonment leaves the local rivals with a point apiece, taking Derbyshire on to five points and Notts to three, each having now completed four matches in the North Group.