Physicians for Human Rights-Israel and the Gaza Community Mental Health Programme appealed on Wednesday to Israel's Supreme Court to stop the supersonic flights, which the United Nations reportedly said is an abuse of human rights.
These extremely loud booms have caused physical and mental harm to the population as well as damage to property.
The Israeli military had no comment. "Because the subject is before the Supreme Court, the response will be given in that framework," the army spokesman's office told an Associated Press reporter.
Israeli warplanes set off sonic booms over Gaza during the day and night, though they refrain from supersonic flights over Israel.
In the statement, the two groups said that according to international law, "the booms are collective punishment against the civilian population and thus illegal".
The groups also state that the violations of the right to health caused by the booms are prohibited by several international conventions, including the International Convention on the Rights of the Child.
The head of the Gaza group, Dr Eyad Sarraj, a psychiatrist, wrote that the sonic booms have serious effects on Gaza children, causing anxiety, panic, fear, poor concentration, stuttering and low academic achievement, according to a statement.
Dr Eyad Sarraj: Miscarriages
increase during sonic booms
He said the number of spontaneous abortions increases during periods of frequent sonic booms.
Over the past week, Israeli jets created 28 sonic booms by flying at high speed and low altitude over the Gaza Strip, sometimes as little as an hour apart through the night, British newspaper The Guardian reports. During five days in late September, the air force caused 29 sonic booms.
In a report, the Palestinian Health Ministry says children are suffering the brunt of the Israeli psychological warfare, wracked by nightmares and fear.
"We have not been able to sleep for four days. The raids ... have a devastating effect on the mental health of my children," Ibtisam Abu Hashem, 32, is quoted by the Health Ministry as saying.
"We have not been able to sleep for four days. The raids have a devastating effect... If we grown-ups are frightened, what can you say about the children?"
Ibtisam Abu Hashem
"If we grown-ups are frightened, what can you say about them [the children]?" she asks.
Although the Israelis say the shockwaves do not cause casualties, doctors at Gaza's Shifa hospital said the overflights had forced women to miscarry, according to The Guardian report.
The number of miscarriages had increased by 40%, according to Jumaa Saqqa, a surgeon and hospital spokesman.
"There were no other symptoms and the rise happened after the sonic booms. We can see no other explanation. The number of patients admitted to the cardiac care unit doubled. Some of them proved to have suffered serious harm," The Guardian reported.
The head of the UN Development Programme in the Gaza Strip, Khaled Abdul Shafi, is quoted by the BBC as saying: "We at the United Nations have already submitted a letter of protest to the Israeli government urging them to stop ... the sonic booming and the air raids immediately."
"[Because] we simply think that this is a violation of basic human rights, especially rights of children to live in peace and to be educated in peace."
Israel has long used sonic booms to rattle Palestinians in times of tension, maintaining the practice since its pullout from Gaza in September.