That's what happened to astronaut Andrew Feustel during a space walk when his eyes got stung by something and started to water.
NASA's lead spacewalk officer in Mission Control, Allison Bolinger, later identified the irritant as an anti-fogging solution that had been applied to the inside of Feustel's helmet. It's essentially off-the-shelf dishwashing soap and occasionally flakes off, if not buffed properly, and can get in a spacewalker's eye.
Feustel managed to rub his eye against a foam block in his helmet — normally used for clearing ears — and said that helped. The spacewalkers noted that tears in space "don't fall off of your eye ... they kind of stay there."
Yup! Another property of gravity that we take for granted.