The hosts started brightly and forced two corners within the opening minute, and their early dominance was rewarded in the fourth minute when Sylvain Wiltord completed a flowing move by firing in right-footed from a tight angle after being set free down the right flank by Dennis Bergkamp.
Arsene Wenger's men seemed set to overrun their Dutch opponents, but Highbury was stunned just twelve minutes later.
A superb ball from Finnish centre-back Petri Pasanen found Nigel de Jong, and after an excellent first touch which took him away from Ashley Cole, the 18-year-old slid a cool left-footed finish past the on-rushing David Seaman.
The second-half proved a scrappy affair with few clear-cut chances, though Ajax custodian Bogdan Lobont was forced into a smart save to deny Gilberto Silva on the hour mark.
The Gunners came closest to breaking the defiant Dutch rearguard when former Ajax idol Dennis Bergkamp fired a shot on the turn against a post from 18 yards.
It was the visitors though who had the best late chance, when substitute Nourdin Boukhari beat Stuart Taylor - who replaced the injured David Seaman at half-time - to a right-wing cross, but ran out of space to steer the ball home, and when Kanu fired over at the death Arsenal's hopes went with his wayward shot.
In the group's other match, Spanish champions Valencia claimed a valuable 1-0 away win at struggling Italian giants Roma.
John Carew struck twelve minutes from time to put Valencia level on five points with both Arsenal and Ajax as Group B takes shape.
For the match summaries click below
Arsenal 1 - 1 Ajax
Roma 0 - 1 Valencia
