Air China included the comments as part of a feature in its in-flight magazine on visiting the city.
It also advised tourists not to go out alone at night, and for females to always be accompanied when travelling.
A London MP has written to the Chinese ambassador to the UK for an apology.
The comments were noticed by Beijing-based producer Haze Fan from US news channel CNBC.
They were published in its monthly Wings Of China magazine and read: "London is generally a safe place to travel, however precautions are needed when entering areas mainly populated by Indians, Pakistanis and black people.
"We advise tourists not to go out alone at night, and females always to be accompanied by another person when travelling."
Air China has not commented on the article.
But MP Virendra Sharma said: "I am shocked and appalled that even today some people would see it as acceptable to write such blatantly untrue and racist statements."
The Labour MP for Ealing Southall, which has a high Indian population, said he had requested for the magazine to be removed from circulation immediately.
"I have invited representatives of Air China to visit my constituency of Ealing Southall to see that a very multi-cultural area is safe, and would be of great value for those visiting London to see.
"I will await their response, and if an appropriate one is not forthcoming I shall feel forced to question whether Air China is a fit company to operate in the UK."
The airline operates two flights per day from Beijing to London Heathrow.
The number of trips to the UK from China rose by 46% last year to 270,000 according to VisitBritain.
The Chinese government has previously raised concerns about how its citizens act abroad.
In 2013, a senior Chinese Communist Party official called for authorities to "guide tourists to conscientiously abide by public order and social ethics, respect local religious beliefs and customs, mind their speech and behaviour... and protect the environment".
A Chinese airline has reportedly warned passengers that "precautions" should be taken when visiting areas in London mainly populated by "Indians, Pakistanis and black people".