At least three people have been killed but some reports suggest the final toll could be higher.
Afghan commandos who landed on the Sardar Daud hospital roof have now killed all the attackers, the interior ministry says.
The so-called Islamic State (IS) group has claimed the attack.
The Taliban has denied any role in the attack, local media reported.
President Ashraf Ghani said the attack at the 400-bed Sardar Daud hospital "trampled all human values".
