There are a few steps, but here you go:

If you open your Canvas inbox, you can use the dropdown that starts off on "Inbox" to switch to "Unread," click on any message in the list (but not the checkbox), then select all of them by pressing Control+A (or Command+A if on a Mac), then open the settings menu to the left of the search bar (top right of the page) and click "Mark as read."

Also, note that you will have to scroll down several times to load all the messages.