Last year's Serie A runners-up won 17 corners and had five shots on target compared to none for the Ukrainians but could not find a way past Dynamo goalkeeper Artur Rudko.
The result left Napoli level at the top of the group on eight points with leaders Benfica, their opponents in their final group game.
A draw would guarantee them a top two place as it would give them a better head-to-head record against the Portuguese champions.
Turkish champions Besiktas, who drew 3-3 with Benfica, have seven points and visit Kiev in their final game, where a win would send them through to the knockout phase.
Dynamo, who have two points and will finish bottom, played with a high back line, inviting Napoli to play through-balls which frustratingly failed to find the target.
Dries Mertens managed to spring the offside trap early on but Rudko made a last-ditch tackle to foil the Belgian, who was playing as a false number nine in place of striker Arkadiusz Milik, out with a long-term knee injury.
Napoli then won a succession of corners which failed to produced anything before Mertens was sent clear again and Rudko this time rushed out of his area to make a risky sliding challenge.
Lorenzo Insigne should have put Napoli ahead when he was sent clear by a Mertens through-ball but he tripped at the vital moment.
Napoli, who won their first two games in the group, continued to push forward in the second half and Rudko made a flying save to turn Marek Hamsik's drive around the post.
Substitute Manolo Gabbiadini curled another effort just wide and then had a shot saved by Rudko but Napoli's challenge petered out.
(Writing by Brian Homewood in Berne, editing by Simon Cambers)
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