The explosions happened near Kabul University and Karte Sakhi shrine, where many people gather every year to mark Nowruz.
Nusrat Rahimi, a spokesman for the Ministry of Interior Affairs said that the blasts had been caused by three remote-controlled explosives.
Immediately there was no claim of responsibility for the attack.
President Ashraf Ghani wrote on Twitter,” as we celebrate this auspicious day to bind us together our fellow citizens witnessed another devastating day in Kabul. We lost peaceful citizens to a coward enemy that knows no bounds. I send my heartfelt condolences to the bereaving families & wish the wounded quick recovery.”