The Gunners' unbeaten start to the season was ended at St James' Park thanks to Anthony Gordon's controversial second-half winner, in which former Arsenal player Willock played a key role.
Willock revealed the abuse he had been sent on Instagram and urged the platform to find those responsible.
"Newcastle United strongly condemns racist abuse sent to Bruno Guimaraes and Joe Willock via social media following Saturday's victory over Arsenal," a Newcastle statement read.
"Our message is clear. There is no room for racism in football or society.
"We are providing support to Bruno and Joe and will work with relevant authorities and social media platforms to identify those responsible so that they can be held to account."
An Arsenal statement read: "We condemn all forms of discrimination and take a zero tolerance approach. We will apply the strongest possible action to anyone we can identify sending hateful messages."
Kick It Out said in a statement: "We send our support to Newcastle's Joe Willock and Bruno Guimaraes after they became the latest players to be targeted with disgusting racial abuse on social media.
"Sadly, this has been an almost weekly occurrence this season, and the costs on players' mental health are huge. That is why the new Online Safety Act must click into gear as soon as possible so that players are better protected.
"Social media companies cannot continue to allow this to happen without consequence, but they can offer better safeguards right now."
The Premier League also offered its help and support and condemned the abuse.
A statement read: "Racism has no place in our game or anywhere in society. We offer our full support to Bruno Guimaraes, Joe Willock, and Newcastle United.
"The Premier League condemns any form of discriminatory abuse and actively works with all players, clubs, platforms, and authorities to help bring offenders of hate crime to justice."