Multimeters use complex integrated circuits that are designed to work with a range of supply voltages, because they mean to be portable and therefore use batteries, and all batteries tend to drop their voltages as they worn out and age.
To accommodate this variable range, the DMM ICs have built-in voltage regulator(s) for important internal circuitry, and use internal self-calibrating techniques to keep their specified accuracy of measurements. And DMMs don't consume any heavy bursts of current when taking measurements (they use steady, continuously running integrators, not some fast high-consuming sampling ADC), so the ESRs of batteries (in fear of voltage sagging) don't make any difference as long as overall battery voltage stays above certain level. (I guess this was the false assumption that led to this inquiry).
Therefore, DMMs are effectively "de-coupled" from power supply, and therefore can use ANY kind of batteries, high-ESR, low-ESR, whatever (as long as their voltage is above certain level) without affecting their functionality. Of course, batteries with low self-discharge would be the best.