The armed man seized the BRED bank branch located on Boulevard de Strasbourg shortly after 5pm local time.
He is understood to have made several demands and police are in negotiations.
The France Blue website reported several customers were inside the bank and were being held hostage.
Police have been mobilised and armed response officers have been called to the scene.
No casualties have been reported.
France 24 tweeted: “A hostage-taking is currently underway in a #Bred bank branch, Boulevard de Strasbourg in #Havre.
“An armed man broke into the bank around 5 pm and is holding 6 people hostage, the neighborhood is cordoned off.”
The National Police of the Seine Maritime tweeted: “Police operation in progress boulevard de Strasbourg @LH_LeHavre
“Respect the security perimeter set up [email protected] PoliceNat76600.”
Another Twitter used posted: “The streets adjoining Boulevard de Strasbourg are currently blocked, all access prohibited between the town hall and the sub-prefecture.”
French news website actu.fr claimed police were concerned in case the hostage taker was also armed with explosives.
Firefighters and ambulances are on the scene.
AFP has reported the man is armed with a handgun and is holding five hostage.
Pictures on social media showed large numbers of emergency vehicles on the scene.
More to follow…