The California-based firm unveiled the five-seater car - its lowest-cost vehicle to date - on Thursday.
Mr Musk tweeted the total reflected the orders received by the end of Saturday.
Pre-orders of the Model 3 will not necessarily all translate into actual sales when the car is released, with first deliveries in late 2017.
It can be ordered in advance in dozens of countries, including the UK, Republic of Ireland, Brazil, India, China and New Zealand.
Potential car owners need to put down $1,000 deposits to reserve their vehicles.
Such has been the interest that Mr Musk tweeted the company was "definitely going to need to rethink production planning".
Mr Musk has said his goal is to produce about 500,000 vehicles a year once production is at full capacity.
The basic model will start at $35,000 (Â£24,423) and have a range of at least 215 miles (346km) per charge.
Tesla delivered 50,580 vehicles last year. Most of those were its Model S saloon, which overtook Nissan's Leaf to become the world's best selling pure-electric vehicle.
But the firm still posted a net loss of $889m (Â£620m) for 2015, partly because it spent $718m on research and development over the period.
It left Tesla with cash reserves of $1.2bn, down from $1.9bn a year earlier.
The company is facing competition from other electric cars with a similar price and range that will become available first, including General Motors' Chevy Bolt and BYD's Qin EV300.
Tesla founder and chief executive Elon Musk says pre-orders of the firm's much-anticipated Model 3 electric car currently total 276,000.