  In this work, we explore the holographic entanglement entropy with an
infinite strip region of the boundary in Horndeski gravity. In our prescription
we consider the spherically and planar topologies black holes in the
AdS$_{4}$/CFT$_{3}$ scenario. In such framework, we show the behavior of the
entanglement entropy in function of the Horndeski parameters. Such parameters
modify the information store of subsystem A, especially when the parameter
$\gamma$ increases the information about the subsystem will also increase or
decrease when it decreases. Thus, with this scheme we compute the first law of
entanglement thermodynamics in Horndeski gravity and we show that a very small
subsystem obeys the analogous property of the first law of thermodynamics if we
excite the system.
