Quartus won't fix skew, exactly. Clock skew usually comes from when a design has a gated/ripple clock that feeds the destination register, but the main clock feeds the source register. When the data transfer between these registers is short, a hold violation can occur. The only way for Quartus to fix the skew would be to add delay on the clock path to the source register. This is most likely on a global, and routed directly to the source register, so it's not a good idea to take that signal off the global. (And you're just moving the problem to the stage before this.)
What Quartus can do is add delay to the data path. This fixes the hold problem, just not the actual clock skew. This is not done by default though. Go to Assignments -> Settings -> Fitter and change the Hold Time Optimization to All Paths(which means it will add delays to internal paths), and also turn on the Optimize Fast Corner checkbox, so it is adding delays to help fix the fast corner.
The reason this is not on by default is it's recommended to not gate clocks from the beginning. If the gated clock could be changed to a clock enable or something like that, then the structure is better from a good design practice standpoint. If Quartus fixed internal hold violations automatically, many designers wouldn't even realize they were gating clocks, or that it's not an ideal thing to do. Of course, I've seen plenty of designs by excellent designers, where they absolutely had to gate the clocks and there was nothing they could do about it, but it's just not recommended if it can be avoided.
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