In a series of tweets Musk said the first deliveries of "electric vehicle for the masses" will be made in late July.
He also said a party to hand over the first 30 Model 3s to customers will be held on July 28.
The Model 3 is to start around $35,000 and with a $7,500 federal electric car tax credit, could cost $27,500.
Tesla says the five-seat car will be able to go 215 miles (346 kilometers) on a single charge and will accelerate from zero to 60 miles per hour in under six seconds.
Musk tweeted the company is on course to produce about 100 cars in August and more than 1,500 in September.
"Looks like we can reach 20,000 Model 3 cars per month in December," he wrote.
The Palo Alto, California-based company intends to make 10,000 Model 3s per week in 2018.
For additional information:
