The 173-metre Lady Zehma was safely grounded and anchored after a rudder failure about 6pm, said the Istanbul governor's office and a shipping company.
The office said no one was hurt and coastguards were attending.
The ship's bow was about 150 metres from shore in the busy Bebek neighbourhood, according to a witness and Refinitiv Eikon data.
Ukraine's grain exports slumped after Russia invaded the country on February 24 and blockaded its Black Sea ports, driving up global food prices and prompting fears of shortages in Africa and the Middle East.
Ukraine and Russia sign grains deal - in pictures
The Joint Co-ordination Centre in Istanbul, which oversees the agreement and comprises UN, Russian, Ukrainian and Turkish officials, told Reuters the ship was "stranded during her passage from the strait and an emergency boarding operation is under way" by Turkish authorities.
This week the co-ordination centre said the Lady Zehma was cleared to depart Ukraine's Chornomorsk port for Ravenna, Italy, with 3,000 tonnes of corn.
Turkey's Tribeca shipping company said it contained 30,274 tonnes of corn.
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As of Wednesday, about 1.55 million tonnes of grain and other foodstuffs had been exported from Ukraine under the deal, while 139 inbound and outbound voyages had been enabled, the centre said.
Such incidents are rare on the picturesque Bosphorus, which divides Turkey's largest city and connects the Black Sea to the Marmara Sea and beyond to the Mediterranean.