West Midlands police said Legia fans threw missiles, including flares, at them, as they tried to force their way through barriers near the Villa Park stadium, Polish state news agency PAP reported.
Four officers were injured, and one was taken to hospital, according to English officials.
The clashes were apparently caused by tensions between the two clubs over the number of tickets allocated to Legia supporters for the match, according to the PAP news agency.
Aston Villa reduced the allocation amid police concerns over possible violence, following unrest at Legia's match against AZ Alkmaar in October, according to news reports.
Tensions 'needlessly heightened' by 'restrictive measures'
The UEFA Conference League Group E game went ahead with away fans blocked from entering the stadium, prompting Legia's officials to boycott the match, the PAP news agency reported.
The Polish club said in a statement that Aston Villa's "restrictive measures" were "unjustified" and "needlessly heightened the pre-match tensions."
Aston Villa condemn Legia Warsaw fans
Meanwhile, Aston Villa said Legia had offered "no assistance" regarding the "serious safety matter of away fans attending Villa Park."
Referring to the clashes before and during the match, the club said: “Aston Villa strongly condemns the behaviour of those visiting supporters and would like to thank West Midlands Police for their professionalism in very difficult circumstances.”
The mayor of the West Midlands region has demanded "strong action" from UEFA, according to the Birmingham Mail website.
UEFA 'strongly condemns the unacceptable violence'
European football's governing body said in a statement: "UEFA strongly condemns the unacceptable violence which occurred around the Aston Villa v Legia Warsaw match. UEFA is in the process of gathering all official reports from the game before deciding on potential next steps."
Thursday's match finished 2-1 to the hosts, meaning Legia are second in Group E of the 2023/2024 UEFA Conference League on nine points.
They next play AZ Alkmaar of the Netherlands in Warsaw on December 14, needing a point to progress to the competition's knock-out stages.
Source: PAP, BBC, Birmingham Mail, dailymail.co.uk