  In this paper, we have investigated the entanglement thermodynamics for
$d$-dimensional charged $AdS$ black hole by studying the holographic
entanglement entropy in different cases. We have first computed the holographic
entanglement entropy in extremal and non-extremal cases in two different
regimes, namely, the low temperature and high temperature limits. We then
obtain the first law of entanglement thermodynamics for boundary field theory
in the low temperature regime in $d$-dimensions.
