Blizzard has confirmed that Diablo 4 will not have an offline mode. Speaking during a panel held at BlizzCon 2019, lead designer Angela Del Priore addressed a question about whether the game can be played solo and whether it will support "a full offline mode."
"We are not going to support an offline mode," Del Priore replied. "But as I said before, nothing in DIablo 4 is going to require partying up. You can play solo and dungeons are private. Campain quest areas will [also] remain private."
So although you will need an internet connection for the game to work, you can still play solo if you don’t want to group up with people. Players who are already familiar with the franchise likely won’t be bothered by this, as the exact same structure has been in place in Diablo 3 for seven years. However, newcomers may not be aware of the fact that online play isn’t mutually exclusive from solo play, and may be deterred from playing if that isn’t made explicitly clear.