The 30-year-old from west London has been arrested on suspicion of being involved in the commission, preparation or instigation of terrorism, the Metropolitan Police said.
The arrest was carried out by officers from the Met’s Counter Terrorism Command who are investigating the terrorist incident in Constitution Hill which resulted in three officers receiving minor injuries on Friday night.
Officers have also been granted a warrant for the further detention of a 26-year-old man who was arrested at the scene.
The man who was arrested on Sunday is being held in custody and an address in west London is being searched.
Shortly after 8.30pm on Friday a suspect deliberately drove a car at police outside Buckingham Palace and then reached for a 4ft sword, police said.
The three officers were injured after they tackled a man who drove a blue Toyota Prius at a marked police vehicle on Friday night.
Commander Dean Haydon, of the Metropolitan Police counter-terrorism branch, said: “Uniformed officers then confronted the driver of the vehicle and during that confrontation the driver reached for a four-foot sword that was in the passenger footwell.
“CS gas was used as part of the arrest and during the struggle the individual repeatedly shouted the words Allahu Akbar.”
Police have been given permission to hold the 26-year-old man from the Luton area until September 1.
He was arrested on suspicion of grievous bodily harm and assault on police and was later further arrested under the Terrorism Act 2000.
It is understood that no members of the Royal Family were in Buckingham Palace when the attack happened.
It took place in a restricted area in Constitution Hill, near Buckingham Palace, when a car deliberately drove at a police van and stopped in front of it.
The officers, who were unarmed police constables and from Westminster borough, got out of the van and approached the car.
Two of the officers were taken by ambulance to hospital with minor cuts and discharged a short time later. The third officer did not need hospital treatment.
With the start of the busy Bank Holiday weekend, which includes the Notting Hill Carnival, people across London will see an increased police presence on the streets.
Mr Haydon urged members of the public to remain vigilant and alert.