A memory module and heat sink arrangement is disclosed to include a memory module, two heat sinks attached to two opposite sides of a memory chip of the memory module, each heat sink having a mounting unit at a top side and multiple retaining spring strips suspending below the mounting unit, and multiple clamps respectively clamped on the two heat sinks and engaged with the retaining spring strips of the two heat sinks and respectively stopped between guide blocks at the two heat sinks to hold respective locating plugs of one of the two heat sinks in engagement with respective locating grooves of the other of the two heat sinks.