At least one visiting supporter was injured as local 'Ultras' pounced on an Irish bar just outside the Old Town area of the Polish capital.
The club indicated fewer than 200 of their fans had made the journey for the game, and several dozen of them had congregated during the day at the popular bar.
Local sources claimed the attack appears to have been pre-planned.
The fanatical element of the notorious Legia support regularly attempt to snatch the banners of opposition supporters, which are then displayed as trophies at Legia's Pepsi Arena.
This is understood to be the motivation for yesterday's mid-afternoon attack.
A Celtic spokesman said: "We are aware of an attack on Celtic supporters and are currently investigating."
The club are still co-operating with enquiries into the major trouble which flared ahead of their Champions League match with Ajax in Amsterdam in November.
However, yesterday's attack was an isolated incident, and no blame has been attached to the Celtic support by the authorities, who are conducting their own investigation.
The authorities will now be extra vigilant ahead of next week's return tie, at Murrayfield on Wednesday, when a large travelling Legia support will be swelled by members of the Polish community in Scotland, who have been snapping up tickets for the tie.