The I too portion of your sentence makes sense and is grammatical. It means
I too [must leave now].
However, this sounds very stilted, and in shortened form, me too is much more common. Some might argue that this latter expression is ungramatical, but it could easily be expanded to a grammatically sound
That goes for me too.
The even makes little sense. As an adverb (which is this usage), it means
Used to emphasize something surprising or extreme: they wore fur hats, even in summer
Used in comparisons for emphasis: he knows even less about it than I do
[Oxford Dictionaries Online]
There is nothing in the limited context that you offer for either example which would support the use of even. I could make up a context that would justify it
A: "I must leave now because I have to be home in 30 minutes."
B: "I had planned to stay, but now even I too must go."