The detainees are Mohammad Mahdi Suleiman, Abdullah Abu Jaber, Mohammad Musleh, Munir Mari and Anas Hanthawi.
According to a report by Alkarama, a Geneva-based Arab rights NGO, Suleiman was arrested in 2013, then 16-years-old, for throwing stones at Israeli settlers. He was sentenced to 15 years in prison.
The Jordan Times, a Jordanian English daily, reported that local news sources claim that few Jordanian detainees have contracted COVID-19.
According to another Sunday press release, the government also holds Israel fully responsible for the conditions of the prisoners, especially amid the coronavirus crisis.
The Times noted that the check-ins by the foreign ministry are "continuous" amid the highest record of percentage of return rates in Israel, despite its lockdown.
Israel has of late faced its own prisoner coronavirus crisis. After witnessing a contentious political debate, the Israel Prison Service announced on Sunday that it would initiate a vaccination campaign for its inmates next week.
The vaccination of the inmates will follow the vaccination of the prison guards.
The announcement was made after Public Security Minister Amir Ohana recanted his objection to vaccinate inmates following public pressure and the objections of both Attorney-General Avichai Mandelblit and Alternate Prime Minister Benny Gantz to his decision.
The Lower House Palestine Committee, comprised of elected officials in Jordan's House of Representatives, on Sunday encouraged human rights organizations to intervene on behalf of both Jordanian and Palestinian prisoners in Israel, according to a press release by the Jordanian government.
Jerusalem Post Staff contributed to this report.