No. Mastodon isn’t E2EE yet.
If you’re needing to send sensitive information, use an E2EE messaging system instead.
In theory, the owner of your server could read at your DMs in the server’s database, and you’ll often hear people say “The admin can read your DMs”. This is not quite the whole story. An admin would need a certain level of technical skill, as there is no way to view DMs in Mastodon’s admin interface. The server owner would have to look directly at the database itself to read a DM, and ignore Mastodon’s interface completely.