The Conservative MP is accused of breaking the law on April 14 while at the wheel of a Skoda on Wandsworth High Street.
Mr Tugendhat, who ran for the Tory leadership after Boris Johnson's departure, used his phone to navigate and had the device in his hand when seen by police.
He is being prosecuted behind closed doors under the single justice procedure at Bromley magistrates court, with a hearing scheduled for Friday.
Police told the court the minister had already tried to pay a fine over the incident and surrendered his driving licence when he was first contacted in April. However, the matter had to be taken to court as he already has six penalty points on his licence, and faces a possible driving ban if convicted.
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