During BlizzCon, Wyatt Cheng (Blizzard’s Lead Game Designer) has confirmed that Diablo Immortal will be an Always-Online game and therefore the title will require an internet connection always active in order to work.
Cheng specifies that it will be possible to deal with solo dungeons, so it will not be mandatory to play multiplayer, but the active connection to the network is required as the game is continuously synchronized with the servers not only to download new data but also for some aspects related to social media and to integrate with Battle.Net, more details will be released soon.
Although you will be able to play alone, to a certain degree (in the demo shown at BlizzCon, the final dungeon could be completed alone or in a party), but the title will not let you play if you do not have an internet connection.
Diablo Immortal was announced on November 2nd during the inaugural conference of the BlizzCon 2018, the reception by the public was rather lukewarm, mainly due to the disappointment regarding the missed reveal of Diablo IV.
Blizzard has stated that there are other Diablo-related projects in the pipeline, Immortal represents only a small part of the expanded Diablo universe.