Lacazette was sent off for elbowing BATE Borisov defender Aleksandar Filipovic during the Gunners' last-32 first leg in Belarus last week.
The 27-year-old missed Thursday's second leg at Emirates Stadium through suspension, with Unai Emery's side winning 3-0 to overturn a 1-0 first-leg deficit and progress to the last 16, where they were drawn to face French side Rennes.
The former Lyon striker was expected to return for that tie next month but UEFA's control, ethics and disciplinary body have decided to increase his ban given the severity of the dismissal.
It means he will now miss both the first leg at Roazhon Park on March 7 as well as the return meeting at the Emirates seven days later.
The news will be a blow to Gunners boss Emery as he looks to win a trophy in his first season in charge at Emirates Stadium.
Lacazette is Arsenal’s second-top scorer this season with 12 goals in 33 appearances in all competitions.
His suspension will put further pressure on Pierre-Emerick Aubameyang, who is top of Arsenal’s scoring charts with 18 goals in all competitions.
No other Gunners player has scored more than five, meaning Emery will desperately hope Aubameyang avoids injury in the coming weeks.
Despite Lacazette’s absence, the Gunners made light work of BATE Borisov on Thursday with goals from Shkodran Mustafi, Sokratis Papastathopoulos and an own goal by Zakhar Volkov securing a 3-1 aggregate win.
Emery certainly knows what it takes to win the competition having lifted the trophy for three seasons in a row with Sevilla between 2014 and 2016.
They reached the semi-finals of the Europa League last season before being beaten by eventual winners Atletico Madrid.