In London, thousands of activists descended on Trafalgar Square, Westminster and the US embassy at the weekend to protest the 46-year-old's death and alleged police brutality in the UK.
Protesters could be heard chanting "black lives matter" and "say my name, George Floyd" in central London, in reference to the campaigning civil rights group.
Video footage on social media shows crowds gathered outside the gates to Downing Street on Sunday, chanting "who do you serve, who do you protect" and "f*** the police".
Mr Javid, former home secretary, said the scene was "very sad to see".
He said on Twitter: "Very sad to see. This is the same police that keeps you and your family safe. The ones that run towards danger when you runaway. Show some goddamn respect."
Some Twitter users criticised Mr Javid's response to the protests.
One Twitter user said: "It’s the same police that disproportionately stops and searches underprivileged black youths. You show some goddamn respect."
Another posted: "Whilst I fully support our police, "show some goddamn respect" really? Look inwards before looking out."
A third wrote: "I think the public response to the establishment might have been a bit improved if the establishment - people like you - had acknowledged George Floyd’s killing at some point this week.
"A former Home Secretary should know better than to protest against a protest. You have a voice."
But others agreed with Mr Javid's comments.
One said: "Just a few years ago, we were praising the police for saving lives during multiple terror attacks. Running towards the danger while we ran away. A shame that this cult forget about this."
Another wrote: "Well said Sajid. Nice to see a senior government figure saying what needs to be said to these people."
The protest on Sunday came after an event in Peckham on Saturday and is set to be followed by several more in the capital this week.
Police arrested 23 people during the protests in London. Scotland Yard said late on Sunday night the arrests were for a range of offences but did not give further details.
Many protests in the US have been peaceful, but others have turned into violent confrontations between demonstrators and police.
A teenage protestor in Detroit was shot dead by an unknown passerby, while a law enforcement officer in Oakland was also killed after being shot.
President Trump has expressed his sorrow at the death of Mr Floyd, but hit out at protestors and threatened Washington activists with "vicious dogs" and ominous weapons" if they entered the White House.
Derek Chauvin has been charged with third-degree murder and manslaughter after he was filmed kneeling on Mr Floyd's neck for around eight minutes.