Mr Yousaf, whose wife and SNP candidate, Nadia El-Nakla, has a brother living in the Palestinian territory, said the family feared for their lives amid escalated tensions in the region.
Rockets were fired from Gaza while Israeli forces bombarded the territory with air strikes in the most serious fighting since the 50-day war in 2014.
The death toll in Gaza rose to 35 Palestinians, including 12 children and three women, according to the health ministry, with some 233 people injured.
Five Israelis, including three women and a child, were killed by rocket fire on Tuesday and early on Wednesday. Dozens of other people were injured.
Israeli air strikes have levelled two apartment towers in the Gaza Strip, where two million Palestinians have lived under an Israeli-Egyptian blockade since Hamas took power in 2007.
Warning shots have allowed civilians to evacuate the buildings, but eyewitnesses said the material losses would be immense.
Mr Yousaf, who was justice secretary before the election, tweeted: “Wife has been in floods of tears all evening. Her brother lives in Gaza with his wife & three young children. He tells us it's raining rockets.
"As a parent, he feels helpless, they cannot leave as they are under blockade. All we can do is pray & hope they are alive in the morning.”
He added this morning: “Thank you to everyone for their kind msgs about my brother-in-law in Gaza. I have passed your kindness and prayers to my wife and her brother who are taking great comfort in them.”
Politicians replied to Mr Yousaf’s comments with messages of support.
Rutherglen MSP Clare Haughey wrote: “Humza, I can’t begin to imagine the fear you’re all going through just now. My thoughts and prayers are with you all.”
MP Chis Law said: “Utterly awful what is unfolding. My thoughts and prayers are with you and your family and Nadia’s family in Gaza.”
Airdrie and Shotts MSP Neil Gray added: “This is so awful, sending all our love to Nadia and all the family.”
Ms El-Nakla, a long-term SNP campaigner, activist and worker, stood as a list MSP in the North East region in last week’s election.
Mr Yousaf’s tweets come as Prime Minister Boris Johnsn urged leaders in Israel and Palestine to "step back from the brink" after violence intensified.
Hamas and other militant groups in Gaza have fired hundreds of rockets at Tel Aviv and other cities.
Israel has responded with air strikes targeting police and security installations, although the Palestinian authorities said there have been civilian casualties.
Mr Johnson said: "I am urging Israel and the Palestinians to step back from the brink and for both sides to show restraint. The UK is deeply concerned by the growing violence and civilian casualties and we want to see an urgent de-escalation of tensions."
The latest upsurge in violence has been triggered by tensions in Jerusalem during the Muslim holy month of Ramadan.
A focal point was the Al-Aqsa mosque compound, a holy site sacred to both Jews and Muslims, while there were also clashes over the threatened eviction of dozens of Palestinian families by Jewish settlers in the Sheikh Jarrar neighbourhood of east Jerusalem.