The telecoms firm is the latest in a long list of major brands who have announced they will not be running adverts on the social media site throughout the month of July in support of the Stop Hate For Profit campaign, which was launched to help stop the spread of racist and hateful content online.
A Verizon spokesperson told the BBC: "Our brand safety standards have not changed. We're pausing our advertising until Facebook can create an acceptable solution that makes us comfortable and is consistent with what we've done with YouTube and other partners."
Carolyn Everson, vice president for Facebook's Global Business Group, reacted: "We respect any brand's decision, and remain focused on the important work of removing hate speech and providing critical voting information. Our conversations with marketers and civil rights organisations are about how, together, we can be a force for good."
Ben & Jerry's and The North Face are among the other firms joining the boycott.
In a statement, the ice cream makers said this week: "Ben & Jerry's stands with our friends at the NAACP and Color of Change, the ADL and all those calling for Facebook to take stronger action to stop its platforms from being used to divide our nation, suppress voters, foment and fan the flames of racism and violence and undermine our democracy.
"Facebook, Inc. must take the clear and unequivocal actions to stop its platform from being used to spread and amplify racism and hate."
Following the death of African American man George Floyd - who died after a police officer knelt on his neck for almost nine minutes during his arrest in Minneapolis, Minnesota, last month - Ben and Jerry's chief executive Matthew McCarthy said "business should be held accountable".
Facebook has insisted they are working on "advancing equity and racial justice".
Mark Zuckerberg's firm - which has pledged $200 million to support black-owned businesses - said: "We're taking steps to review our policies, ensure diversity and transparency when making decisions on how we apply our policies, and advance racial justice and voter engagement on our platform."