The Justice Minister tweeted on Tuesday evening: “Wife has been in floods of tears all evening.
"Her brother lives in Gaza with his wife and 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 and hope they are alive in the morning.”
Mr Yousaf added on Wednesday 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.
“I hope the international community intervenes and actually tackles the root of this conflict.”
The PA have reported that the death toll in Gaza rose to 35 Palestinians, including 10 children, according to the Health Ministry, which said more than 200 people were wounded.
Five Israelis, including three women and a child, were killed by rocket fire on Tuesday and early on Wednesday, while dozens of others were injured.
In the West Bank, meanwhile, a 26-year-old Palestinian was killed during clashes with Israeli troops that entered al-Fawar refugee camp in southern Hebron, Palestine's health ministry said.
In another sign of widening unrest, demonstrations erupted in Arab communities across Israel, where protesters set dozens of vehicles on fire in confrontations with police.
The UN Security Council planned to hold its second closed emergency meeting in three days on Wednesday on the escalating violence, an indication of growing international concern.
Council diplomats, speaking on condition of anonymity because discussions have been private, said the UN's most powerful body did not issue a statement because of US concerns that it could escalate tensions.
The fighting between Israel and Hamas was the most intense since a 50-day war in the summer of 2014.
The Prime Minister called for restraint and said the UK is alarmed at the mounting toll of 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."
Additional reporting by PA