The comic, who has a string of convictions for hate speech in his homeland, performed the stiff-armed gesture after naming the queen in a rant during a show in the Swiss town of Nyon.
Dieudonne invented the allegedly anti-Semitic"quenelle" gesture that Anelka used during a goal celebration in December, landing the striker with a charge from English footballing authorities.
"We can confirm that Mr. Dieudonne is subject to an exclusion order," a Home Office spokeswoman said in a statement.
"The home secretary (Theresa May) will seek to exclude an individual from the UK if she considers that there are public policy or public security reasons to do so."
British media last week quoted Dieudonne as saying that he was planning to perform a show in Britain and hold a press conference in support of his friend, former French international Anelka.
The Home Office refused to give further details on the order banning from Britain.
But a British government source told AFP on condition of anonymity: "The reason for the exclusion order is that he was going to come to the UK."
Dieudonne, who also faces accusations of fraud at home, says he is being persecuted by the French authorities.
"So many things have happened over the past year. Just today... Shit, what have I done? I don't know," he said during his show in Nyon.
His lawyer Jacques Verdier said he did not know if his client had actually intended to go to London.
He said that the ban showed British authorities were "nervous" and added that "it's appalling but nothing surprises us at the moment."
Trademark stiff-armed gesture
Anelka has been charged by the Football Association, the sport's governing body in England, after he made the "quenelle" gesture, which critics say is anti-Semitic but Dieudonne insists is anti-establishment.
The West Bromwich Albion striker made the gesture during a goal celebration after scoring against West Ham during an English Premier League match on December 28.
Anelka denies the charge, saying he is neither anti-Semitic nor racist, and that he made the gesture in support of Dieudonne.
Britain is using new laws to combat anti Semitism which were brought in last year and has used exclusion orders on rare occasions in recent years to keep out public figures deemed as having extreme views.
France has in recent weeks intensified a crackdown on Dieudonne, who has been widely accused of promoting anti-Semitism and has been convicted in France for hate speech and other related offences.
The French government in December succeeded in preventing him from starting a nationwide tour of a new show, "The Wall", because of its perceived anti-Jewish content.
Last week French police seized €650,000 and $15,000 in cash during a raid on his house as part of a probe into suspected fraud.
Authorities are currently trying to force Dieudonne to pay more than €65,000 in outstanding fines related to his convictions and suspect that the 47-year-old was planning to fraudulently declare himself bankrupt.
The "quenelle" is Dieudonne's trademark stiff-armed gesture that critics say is a disguised Nazi salute but that he defends as a generic "up yours" to the French establishment.
Some followers of Dieudonne have been photographed doing the quenelle at sites including Auschwitz, synagogues and outside a Jewish school in Toulouse where a rabbi and three children were shot dead by Islamist gunman Mohamed Merah in 2012.