Shares in the fast food chain are trading at around $48.5 per share on the New York Stock Exchange under the ticker symbol "SHAK", valuing the company at more than $1bn (£665m).
The burger chain sold 5m shares, raising $105m and giving it an initial valuation of $745.5m.
Restaurateur Danny Meyer, who grew Shake Shack from humble beginnings in a hot dog cart in Madison Square Garden, said the blockbuster valuation didn't put any pressure on the company.
Myer told CNBC: "We cook one burger at a time with one smile at a time, and I don't know how you value that."
Shake Shack now has 63 stores worldwide, including a prime spot in Covent Garden in London. Its burgers and milkshakes helped the company generate more than $80m (£52m) in sales in the first nine months of 2014.
To celebrate today's milestone, a Shake Shack truck pulled up outside the New York Stock Exchange and gave away free burgers for two hours.