Turkish President Recep Tayyip Erdogan confirmed there had been several fatalities in the twin bomb attacks.
"Unfortunately we have martrys and wounded" as a result of twin blasts, Erdogan said in a statement.
Armed police sealed off streets around the Vodafone Arena, home to the Besiktas football team. Ten suspects have been detained.
TV footage showed what appeared to be the wreckage of a burned out car and two separate fires on the road outside the stadium.
Turkish Transport Minister Ahmet Arslan said on Twitter that it was a terrorist attack.
There was no immediate claim of responsibility. Omer Yilmiz, a cleaner at the nearby Dolmabahce mosque, said: "It was like hell. The flames went all the way up to the sky.
"I was drinking tea at the cafe next to the mosque. People ducked under the tables, women began crying. Football fans drinking tea at the cafe sought shelter, it was horrible."
It happened after Besiktas beat visitors Bursaspor 2-1 in the Turkish Super League. More than a dozen ambulances arrived on a street next to the stadium
Turkey has experienced a bloody year of militant attacks in its two biggest cities that have left dozens dead and put the country on high alert.
Kurdish militants have twice struck in Ankara, while suspected Isis (Islamic State) suicide bombers have hit Istanbul on three occasions.
Last week a newly identified spokesman for Isis urged sympathisers around the world to carry out a fresh wave of attacks, singling out Turkish diplomatic, military and financial interests as the Islamists' preferred targets.
Abi al-Hassan al-Muhajer said Isis supporters would target "the secular, apostate Turkish Government in every security, military, economic and media establishment, including every embassy and consulate, that represents it in all countries of the world".
In June, 47 people were killed in a triple suicide bombing and gun attack at Istanbul's Ataturk airport, with authorities pointing the finger at Isis.
Another 57 people, 34 of them children, were killed in August in a suicide attack by an Islamic State-linked bomber at a Kurdish wedding in the southeastern city of Gaziantep.
The country is also still reeling from a failed July 15 coup blamed on the US-based Islamic preacher Fethullah Gulen that has been followed by a relentless purge of his alleged supporters from state institutions.