You can host your DApp in cloud. It is important to know what exactly you want to host there. Most probably you will have two parts, web application and blockchain.
- blockchain - you can also host it in cloud, you need to run VM. You can run Ethereum full node there. I'm not sure that you want to handle it, because you need quite lots of space. You can use Infura instead.
I didn't get such blockchain environment like Heroku
I never saw hosting with prepared blockchain, usually everyone run it for their own.
In Azure you can find prepared VM snapshots for Ethereum, but you need to install it on your subscription, manage it and pay for it.