Supporters in the away end could be seen making the obscene actions during the Gunners’ 3-1 win.
UEFA have been made aware of the incident, filmed by a fan and posted on social media, and are expected to open an investigation.
Six Valencia supporters were ejected from the stadium on Thursday night, although it is not known whether this was in connection with making racist gestures.
An Arsenal statement said: "We utterly condemn such behaviour. It has no place in society or football. We continue to encourage fans to report incidents and to provide witness statements so effective action can be taken."
Kick it Out, the FA’s anti-discrimination body, have also condemned the offending fans in a statement, saying: "These blatant racist gestures are shocking and inexcusable.
"We hope the relevant authorities identify the perpetrators and take the strongest possible punishment. There is no place for any form of discrimination in football or society."
Mouctar Diakhaby's header put Valencia in front on Thursday night in north London, before two goals from Alexandre Lacazette turned the game in the hosts’ favour before half time.
Pierre-Emerick Aubameyang completed the victory in the last minute to set Arsenal up for the second leg in Spain next week, but it was for events in the stands that the night will likely come to be remembered.
The incident marks another miserable low in the fight against racism inside European football stadiums.
England defender Danny Rose said he was “lost for words” last week after the Montenegrin Football Federation
Rose, Raheem Sterling and Callum Hudson-Odoi were all targeted by home fans during England’s 5-1 Euro 2020 qualifying win in the Montenegro capital, yet the punishment meted out by UEFA has widely been condemned as being unfit for the purpose of dissuading offenders.
In Italy, Napoli’s Kalidou Koulibaly and Juventus’s Moise Kean have both been targeted by supporters at Serie A matches, with debates raging throughout Italian football over whether players would be justified in walking off the pitch if subjected to racist abuse.