Mr Musk walked away from his $44bn (£36bn) bid to buy Twitter earlier in July, prompting the company to sue him.
Twitter hopes that the court will order Mr Musk to complete the takeover at the agreed price of $54.20 per share.
The tech billionaire has accused Twitter of withholding information about fake accounts.
His legal team has called for the trial to be held early next year due to its complexities, but Twitter asked for a September date.
On Tuesday, a judge in the state of Delaware agreed with the company and said a delay to the trial would cast a "cloud of uncertainty".
"Delay threatens irreparable harm," Chancellor Kathaleen St Jude McCormick said. "The longer the delay, the greater the risk."
The lawsuit accused Mr Musk of a "long list" of violations ahead of the potential merger and argued that he had "cast a pall" over the company.
At the hearing on Tuesday, Twitter's lead counsel William Savitt said the ongoing uncertainty about whether the takeover would go forward or not "inflicts harm on Twitter everyday".