Police also confirmed two men were arrested after David Bryan, who was running the line in front of Spurs fans, was hit by a smoke bomb thrown from the visiting supporters' section at Villa Park.
The restart was delayed as the smoking missile was removed but Bryan was unharmed and able to continue.
An FA spokesman said: "The FA will investigate this matter, which is unacceptable. We will await the match officials' report and will be speaking to the clubs.
"Such incidents highlight the dangers of pyrotechnics being used in a football stadium."
Police officers and stewards moved in to remove supporters from the away fans' section, which is housed in the Doug Ellis Stand.
West Midlands Police later confirmed two men had been arrested in relation to the incident, which was also captured by television cameras.
"Police have arrested 2 men after a lit flare was thrown on the pitch during the Villa v Spurs game - the flare hit a linesman," a statement, released via Twitter, read.
"The two men aged 25 and 47 were arrested following the incident at Villa Park, fortunately the linesman wasn't injured."
Tottenham went on to win the match 2-0 with a further goal from Roberto Soldado.
Spurs boss Andre Villas-Boas condemned the people responsible.
He said: "Obviously it is not great to see. It should be avoided completely. I think it touched the linesman. I think situations like this do not have a place in football. I sincerely hope it does not happen again."