def run(self):
        self.finished.wait(self.interval)
        if not self.finished.isSet():
            self.function(*self.args, **self.kwargs)
        self.finished.set()

I think the function run() should be modified to like this below:

def run(self):
        while not self.finished.isSet():
            self.finished.wait(self.interval)
            self.function(*self.args, **self.kwargs)

In this case, it can still run on next 'interval', and next's next...

Note that doing this would change the class semantics.
Timer "[...] represents an action that should be run only after a 
certain amount of time has passed — a timer." and the example clearly 
shows that the action is run *once*. 

Timer is basically an example of how to write custom Thread 
subclasses; if you want a "repetitive action", you may easily write a 
subclass based on the code you posted. Not every useful class must be 
in the standard library...

Indeed, Timer is designed to run the function once.