Erdogan said before he departed Turkey that the “vile attack” that killed at least six people in the heart of the city had “a smell of terror”.
The explosion tore through a busy Istanbul shopping street on Sunday, killing six and wounding dozens.
Police cordoned off an area around Istiklal, where there were dense crowds on Sunday afternoon, and helicopters flew over the city center as sirens sounded.
Turkey’s interior minister accused the Kurdistan Workers’ Party (PKK) of responsibility.
The PKK, blacklisted as a terrorist group by Ankara as well as its Western allies, has kept up a deadly insurgency for Kurdish self-rule in southeastern Turkey since the 1980s.
“The person who planted the bomb has been arrested,” interior minister Suleyman Soylu said in a statement broadcast by the official Anadolu news agency.
Regularly targeted by Turkish military operations, the group is also at the heart of a tussle between Sweden and Turkey, which has been blocking Stockholm’s entry into NATO since May, accusing it of leniency towards the PKK.