The 18-year-old made his senior debut last season but has been injured for much of the current campaign.
"The Danish doctors didn't think he could survive. I couldn't stop crying when I arrived at the training ground. My father could die," Højbjerg in an interview with Danish TV DR.
"I'm 18 and here I am. I'm injured and I'm alone. What shall I do?"
Guardiola then called Højbjerg to speak to the young Dane personally.
Højbjerg continued: "He said: 'I've heard about your father and I'm extremely upset about it. Let's have a chat.'
"And then I just started to cry and said I was bewildered and scared. Then he said to me: 'You have to stand by the people who are close to you, even if your work suffers.
"Then he began to cry and didn't know what to say."
The Bundesliga champions then arranged for the player's father to be flown to Germany to receive treatment.
"Now they say my father has a reasonable chance of survival," said Højbjerg.