Tesla did not immediately respond to requests for comment.
Musk has repeatedly scaled back Tesla's production schedule, something he recently referred to as a "time shift".
"To be clear, we will continue to hire rapidly in critical hourly and salaried positions to support the Model 3 production ramp and future product development".
Tesla also missed Model 3 production goals for the first quarter in April.
In his email to staff, Musk said Tesla was "flattening the management structure to improve communication", combining functions and trimming activities "not vital to the success of our mission" in the reorganisation.
Tesla's shares fell by 5% afterwards.
"What's actually wonderful about this accident is that a Model S hit a fire truck at 60 miles per hour and the driver only broke an ankle".More news: South Dakota Senator Mike Rounds Undecided on Gina Haspel Vote
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Complicating Tesla's problems, however, have been reports of a series of recent crashes that have resulted in several deaths and injuries.
In March, a Tesla Model X was on autopilot mode when it collided with a barrier on Highway 101 in Mountain View, Calif., killing the 38-year-old driver. The Tesla's driver suffered a broken right ankle, and the driver of the Unified Fire Authority mechanic truck didn't require treatment, Winkler said.
A day later, another engineer, Matthew Schwall, who was also Tesla's primary technical contact with the National Transportation Safety Board, left for competitor Waymo, an offshoot of Google, the Wall Street Journal reported. The NTSB previously criticized Autopilot for playing a role in a fatal, 2016 crash.
The crash, in which the Tesla driver was injured, comes as federal safety agencies investigate the performance of Tesla's semi-autonomous driving system.
The driver in that incident died, but Tesla said he was pulled from the vehicle before it caught fire.
The South African-born executive again took to Twitter in response to coverage of the Utah crash.
Responding to media coverage of the accident, Musk tweeted: "it's super messed up that a Tesla crash resulting in a broken ankle is front page news and the ~40,000 people who died in United States auto accidents alone in past year get nearly no coverage". Accidents that previous year resulted in 40,000 US deaths, he added "get nearly no coverage".