The pair clashed on the show on Tuesday over how many logs to use in a fire.
The Scottish Labour Lothian MSP, a late entry to the jungle, tried to use all the wood available at once but was challenged by Khan.
In a conversation with fellow contestant Georgia Toffolo, the boxer had to be reminded of Ms Dugdale’s name before criticising her.
Khan also said that she would be the first to leave the camp.
He said: “Kezia, all she does is sleep. She never smiles.
“The first one Kez 100 per cent, she’s always moody, is she allowed to smile? Vote Kez now.”
Later in Thursday’s show, comedian Iain Lee praised her cooking.