Footballers Marcus Rashford, Anthony Martial, Axel Tuanzebe (twice) and Lauren James as well as West Bromwich Albion's Romaine Sawyers, Chelsea's Reece James and Southampton's Alex Jankewitz have all been subjected to racist abuse online over the past few months.
In a statement on his social media platforms, Henry wrote: "Hi Guys. From tomorrow morning I will be removing myself from social media until the people in power are able to regulate their platforms with the same vigour and ferocity that they currently do when you infringe copyright.
"The sheer volume of racism, bullying and resulting mental torture to individuals is too toxic to ignore. There HAS to be some accountability.
"It is far too easy to create an account, use it to bully and harass without consequence and still remain anonymous.
"Until this changes, I will be disabling my accounts across all social platforms. I'm hoping this happens soon."
The English Football Association has also called on social media companies to introduce identification for accounts on their platforms after an increase in online abuse aimed at footballers.
Premier League referee Mike Dean also recently received death threats on social media.
Last month, Instagram announced a series of measures to address online abuse, including removing accounts of people who send abusive messages and developing new controls to help reduce the abuse people see.
Twitter said in 2019 that "vile content has no place on our service" after it took action on more than 700 cases of "abuse and hateful conduct" related to football in Britain in two weeks and promised to continue its efforts to curb the problem.