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A statement from F1's governing body the FIA said the man gained "unauthorised access" to the circuit.
The FIA said: "We are awaiting a full report from the clerk of the course in order to determine the circumstances surrounding this incident."
Race winner Sebastian Vettel said: "Fortunately nothing happened to us or him. It's not what you want to see."
It is the second time this year someone has gained access to a track during a grand prix weekend, with a spectator running across the circuit during practice at the Chinese Grand Prix in April.
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It is also the third time in recent history that a track invader has disrupted a grand prix.
In 2003, a man wearing a kilt ran across the track during the British Grand Prix.
And a disaffected former Mercedes employee invaded the track during the 2000 race in Germany.
Vettel, who drives for Ferrari, made a joke about this incident, which has been reported to involve an English tourist.
"When I was watching F1 there was a scene in Hockenheim and then a couple of years later in Silverstone," he said.
"This guy was fairly boring. He could have dressed a little funny or something.
"Now we are joking about it, but it is fairly serious."
Red Bull's Daniel Ricciardo, who finished second, added: "He was on his phone taking pictures, probably for Instagram or something.
"I hope he got some more followers because it's got to be worth a night in prison."

The 80-year-old Tokyo market is known for its tuna auctions which supply many of the capital's top sushi restaurants.
Smoke could be seen billowing from shops on the outskirts of the market on Thursday, as dozens of fire engines tackled the flames.
The fire was out by Thursday night and there were no reports of injuries.
Tsukiji's interior industrial market - where the famous tuna auctions take place - was undamaged and the area was open to tourists as usual.
The blaze broke out at about 16:50 local time (07:50 GMT), Japanese broadcaster NHK said, in the outer region of the market and close to the surrounding area's narrow streets.
The area is home to many sushi restaurants and shops, some of which have been evacuated, NHK reports.
The cause of the fire is not yet known. The blaze seems to have affected several old wooden buildings.
The market was constructed in 1935, in the aftermath of the great Kanto earthquake of 1923, and built largely from corrugated iron sheds.
Today, it is a sprawling, busy market, but is seen by many as rundown and overcrowded.
Nonetheless, its enormous volume and variety of produce means it receives tens of thousands of tourist visitors each year.
The market is due to be moved by the end of 2017.
Efforts to move the market to a more modern location have been met with resistance by many of the workers, some of whom have been in the family business for generations.
Tokyo's governor, Yuriko Koike, has previously said the market needs to be rebuilt because of its age - and the associated risk of it being vulnerable to earthquakes, which are not uncommon in Japan.

The video shows two masked men firing a volley of shots into the air as two children stand nearby.
It was posted on a YouTube channel called IRSP (Irish Republican Socialist Party) Media Belfast.
The channel indicates that the video was filmed at the funeral of Barry McMullan on Monday.
The published description of the video reads: "Irish Republican Socialist Movement lay Comrade Barry McMullan to rest with full honors (sic). Belfast, June 26th 2017."
Det Ch Insp Gary Reid said: "Police are aware of the footage showing shots apparently being fired by masked men in west Belfast in recent days.
"An investigation is underway."
A 27-year-old man who invaded the Formula 1 track during the Singapore Grand Prix has been arrested.
[NEXT_CONCEPT]
Firefighters have extinguished a blaze at Japan's famous Tsukiji fish market - the largest in the world and a top tourist attraction.
[NEXT_CONCEPT]
Police have launched an investigation after video emerged of shots apparently being fired at a republican funeral in west Belfast.