The Gunners had fought back to lead in the first leg of their second-round qualifier at Meadow Park but were pegged back by a late equaliser as the Dutch side claimed a strong result.
Arsenal fell behind to a Romee Leuchter effort after 17 minutes at Boreham Wood but levelled with a Stina Blackstenius strike just six minutes later.
Kim Little then gave the hosts the lead from the penalty spot just before the hour but Leuchter’s second of the evening seven minutes from time kept Ajax firmly in the tie.
Substitute Katie McCabe thought she had claimed a late winner for Arsenal but her effort was ruled out for offside.
The Gunners now turn their attention to a north London derby as they welcome Tottenham to the Emirates on Saturday, with more than 45,000 tickets sold, before travelling to the Netherlands looking for a positive result against Ajax in the second leg.
Scottish champions Rangers will need to overturn a 3-2 deficit to advance after they were beaten by Benfica despite two goals from Kayla McCoy in a thriller at Ibrox. She heading them ahead after 25 minutes but Benfica hit back with an Ana Vitoria double.
McCoy responded to level the scores again but the Portuguese side, who also hit the woodwork twice, won it on 79 minutes when Victoria Esson failed to keep a out a ball that took a looping deflection off Lisa Martinez. The winner was later credited to Benfica captain Pauleta.