The company joined rivals PG Tips in showing #solidaritea with anti-racism protesters who have turned out for demonstrations across the UK.
Protests began in the US after a video emerged of Mr Floyd, 46, being arrested on May 25 in Minneapolis, USA.
Phone footage showed him gasping that he could not breathe during the arrest by four officers.
They have since been charged over the death, which sparked days of protest in the US and demonstrations across the world.
Laura Towler, a Yorkshire-based YouTuber who has been listed as one of the most influential far-right vloggers in the UK, tweeted that she was 'chuffed' with Yorkshire Tea for not posting publicly in support of the movement.
But the brand, which is owned by Bettys and Taylors of Harrogate, hit back at the comment on Twitter.
Yorkshire Tea replied: "Please don't buy our tea again.
"We're taking some time to educate ourselves and plan proper action before we post. We stand against racism. #BlackLivesMatter"
The response has now been liked more than 50,000 times and PG Tips joined its rivals in supporting the Black Lives Matter movement.
PG Tips posted: "If you are boycotting teas that stand against racism, you're going to have to find two new tea brands now #BlackLivesMatter #Solidaritea"
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