Does VSTO run on Windows Azure?

Joni and Joe are correct. VSTO will not run on Azure.

I believe you're looking for the Open XML SDK. That lets you create Excel or other Office files from .NET without using Office automation.

Edit: Here's one option I have considered for those times when the Open XML SDK just doesn't have the functionality I can get from accessing an Office app's object model directly. Set up a machine outside of Azure that operates just as an Azure worker role would by processing messages from an Azure Queue. Since the app on that machine could be setup to execute tasks sequentially, you should be able to get away with things that wouldn't be advisable if you were trying to execute an Office app from a web role. This machine could be in your data center, or you could use an Azure VM so that you could install Office. If that VM was creating and/or reading Excel documents, then just use Azure Blob storage to store the documents.

If the machine running Office is outside of Azure, you will incur additional bandwidth costs for all the data coming in and out of Azure.

I tested this and apparently it won't work, VSTO requires Office to be installed.

I've been successful with generating Excel Spreadsheets in Azure using EPPlus open source project. It builds on the OpenXML SDK, but is much simpler to use.

I've been deploying the code to Worker Role instead of Web Role (as per Lokad.CQRS for Azure architecture) in order to pregenerate reports, so that the application would be more scalable. And the only required assembly was the Epplus.dll.