Some things suggest that Tsunade might be related to Naruto (possibly grandmother like people have mentioned) and other things suggest that she isn't.

An 'isn't' clue: The fact that she had no idea who Naruto was when they met in that bar, she said something like "who's this idiot?"

An 'is' clue: The fact that her brother really, really looks like Naruto, it could be a family resemblance. A sneaky clue by Kishimoto? Or a red herring?