Vilanova, who was Guardiola's assistant at Barcelona before replacing him as coach, left his position at Camp Nou on Friday.
And the Bayern Munich manager believes the 44-year-old had the strength to fight the illness.
"He's my friend, I love him greatly and I hope the best for him in the future, with his family. He's a very strong person in my opinion," Guardiola explained.
Guardiola's side reached the final of the pre-season Telekom Cup on Friday after a win over Hamburg on Saturday.
After the win, the Spaniard praised his side's spirit while also confirming that close-season capture Mario Goetze will not feature against his former club Borussia Dortmund in next weekend's Super Cup.
"Goetze is not ready. I hope next time Basti (Schweinsteiger) will be," he said.
"The attitude of the whole team is incredible in my opinion. I've said it before, Jupp Heynckes has spoken about the attitude of the players on numerous occasions.
"I am so surprised by this. We have to move forward, that's our route, but after three weeks I am happy.
"But next week, in seven days we have the final of the super cup against a super team BVB, and we need to prepare for this."comments