The husband and wife's 3-year-old son was involved in a hostage situation following the attack but was unharmed. The attacker was shot dead by police.
The claim of responsibility came from Amaq Agency, the Islamic State-supporting news wire and propaganda mouthpiece that operates on social networks like Telegram and Twitter to spread news instantly around the globe.
On Sunday, the Islamic State claimed responsibility in identical fashion for the terrorist attack at an Orlando gay night club that left at least 50 dead. It stands as the deadliest mass shooting in U.S. history.
Following the Orlando attack, Islamic State supporters attempted to flood social media with propaganda celebrating the act and threatening further violence. In the wake of two more killings in Paris, similar propaganda will likely follow quickly behind.