There have been no reports of injuries, say Japanese officials.
A fire official told AFP news agency the blaze started at a two-metre-tall (6.7ft) cooling tower at a factory owned by a unit of Nippon Steel.
Haneda airport is about 25km (15.5 miles) from central Tokyo. The steel plant is situated in the city of Kawasaki, which is next to the airport.
Passengers at the airport uploaded pictures of the fire on social media showing large plumes of black smoke.
One Twitter user wrote (in Japanese): "I was about to board my flight at a gate at Haneda airport when I realised many people were looking outside the window so I went over and realised there was a huge fire.
"Our flight was delayed by 15 to 20 minutes, and the pilot said it was partly because of the fire (but no major issue).
"Because of recent news about explosions in Yokosuka and China, I started wondering if it was something similar and people were looking nervous.
"The pilot also said they received a lot of enquiries [about whether] there was any accident."
The fire spread to a factory next door operated by consumer goods company Kao, and 600 employees were evacuated, Japan's public broadcaster NHK reported.
There was no immediate impact on the airport, NHK also said.
One passenger, Darren Pauls, said on Twitter that operations appeared unaffected and the airport train was still running.
It was the second large fire to break out in Japan on Monday, following a blast at a US military base in Sagamihara which has been extinguished.
The US Army said the warehouse stored compressed gases including nitrogen, oxygen and freon. Authorities are still investigating the cause of the blast.
A large fire has broken out at a steel plant near Haneda airport south of the Japanese capital, Tokyo.