Musk also confirmed that the next-generation Tesla Roadster, which he described as "an entirely new car," will be out in four years.
"Ludicrous Speed" is a $10,000 option for the Model S.
It provides a 10 percent improvement in the 0-60-mph time to 2.8 seconds and a quarter-mile time of 10.9 seconds, according to the automaker. Time to 155 mph is now 20 percent faster than a standard Model S.
Musk described the acceleration as "faster than falling."
Existing P85D owners will be offered the upgraded pack electronics for the next six months at $5,000, plus installation labor.
Musk said the 2016 Tesla Model X midsize electric SUV, which is on track for the first deliveries in two months, will also have optional Ludicrous Speed, but due to the vehicle's weight and center of gravity, it will be slightly less quick, with a 0-60-mph time of around 3.3 seconds.
In addition to "Ludicrous Speed," a battery upgrade from 85 to 90 kWh is available to Model S owners for $3,000.
Musk said the new battery will provide up to 15 miles of additional range. The current longest-range Model S, the 85D, will have approximately 300 miles of highway range at 65 mph with the upgrade.
Tesla also is appealing to value-minded shoppers.
It will offer a single-motor version of the 70 kWh Model S for $5,000 less than the dual-motor version. That version will cost $70,000, but Musk said buyers can expect to pay about $50,000, factoring in incentives and gas savings.
Pricing does not include the $1,170 destination charge.
Edmunds says: The increased driving range and affordability of the Tesla Model S will be welcome news to car shoppers in the market for an electric vehicle.