Installing 1600Mhz memory in a Mac Mini that uses 1066Mhz memory

I have an old Mac Mini (2009, Core 2 Duo) which uses 1066 Mhz DDR3 RAM modules. However, I haven’t been able to find them near me; the closest I’ve found are 1600Mhz modules, which have otherwise the right specs (DDR3, SO-DIMM, etc.). Will it work?

(I thought there would be no problem, but the guy in the store told me that some computers might not boot if they detect a faster memory than they are prepared to use. Can anyone confirm?)