Musk was responding to a tweet from a Tesla owner who said he was experiencing a server error when connecting to his Model 3 through the iOS app in Seoul, South Korea.
Elektrik was the first to report on the holidays.
Downdetector, which monitors outages, reported that about 500 users said they encountered an error around 21:40 GMT.
The site tracks crashes by compiling reports from a series of sources, including errors reported by users on its platform.
By 0220 GMT, the number of notifications was at just over 60.
“We apologize,” Musk said. “We will take measures to ensure this does not happen again.”