Wizard is currently concentrating on a spell. Wimpling has a -1 Strength modifier, and makes a melee attack on Wizard. The attack hits, but Wimpling rolls a 1 on the damage roll, meaning that after applying his Strength modifier, he deals 0 damage.
Per the SRD, Damage Rolls (and in more recent Player's Handbook printings):
With a penalty, it is possible to deal 0 damage, but never negative damage.
From the Spellcasting chapter, Concentration:
The following factors can break concentration:
Taking damage. Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration. The DC equals 10 or half the damage you take, whichever number is higher. If you take damage from multiple sources, such as an arrow and a dragon’s breath, you make a separate saving throw for each source of damage.
But I'm not sure if "dealing 0 damage" means that the target "takes damage". Does Wizard need to make a Constitution saving throw to continue concentrating on the spell?
I'd prefer official sources or references if available. If there aren't any, then I would accept any semi-official or well-informed well-reasoned arguments, preferably backed up by whatever evidence is available.