In October, one Tesla driver asked him: "Can you put a dog mode on the Tesla Model 3.
"Where the music plays and the airconditioning is on, with a display on screen saying 'I'm fine my owner will be right back'?"
Musk replied: "Yes".
New features are typically added to Teslas via over-the-air software updates.
'Dog mode' will likely be an extension of Tesla's Cabin Overheat Protection System.
This already prevents temperatures inside the car from reaching unsafe levels when kids or pets are inside.
But the screen in Tesla models is likely to now flash a message to pedestrians informing them that the pet inside is safe.
The "dog mode" update will be launched at the same time as a "sentry mode" — designed to ward off would-be thieves.
Mid-week, Musk responded to a relative of a Tesla owner whose car window had been smashed.
The Twitter-user wrote: "Any update on sentry mode? Brother in law has his window broken into twice in the past two months."
Musk replied: "Sentry Mode (and Dog Mode) roll out next week."
Sentry Mode will use the dashcam to record footage in the event of an attempted break-in.
And it is rumoured the car will play loud classical music through the stereo system to draw attention to the intruder and encourage passersby to call the police.