The militant group said it killed many officers and wounded others, an account not confirmed by authorities.
The blast was the third incident involving explosives in the capital in a week.
Police shot and killed a suspected militant who tried to cross a security checkpoint on a motorcycle armed with explosives in Dhaka's Khilgaon area on Saturday.
A day before that, a suicide bomber blew himself up at a security forces base, again near Dhaka's airport , injuring two police officers.
The militants named this Friday's attacker as Abu Mohammed al-Bengali and said he had detonated his explosive jacket in the midst of police officers it dismissed as "apostates" in a message posted on supporters' social media accounts.
Dhaka city police chief, Asaduzzaman Mia, gave a different account at the scene, telling reporters the man had been carrying the bomb which exploded as he tried to hide it from police.
Islamic State and Al Qaeda have made competing claims over killings of foreigners, liberals and members of religious minorities in Bangladesh , a mostly Muslim country of 160 million people.
Authorities have consistently ruled out the presence of such groups, blaming domestic militants instead.