They are also scheduled to meet with Morocco's King Mohammed VI, who has said Morocco would remain an advocate for Palestinians.
Morocco followed the United Arab Emirates, Bahrain and Sudan in moving toward normal relations with Israel.
Kushner and Shabbat landed in Rabat on Tuesday on the first commercial flight between Israel and Morocco.
As a part of Rabat's deal, the USA has agreed to recognise Moroccan sovereignty over the entirety of Western Sahara, a disputed territory that was annexed in 1975 following an end to Spanish colonial rule.
Ben-Shabbat says the agreements that are being signed between the two countries deal with tourism, agriculture and other issues.
While the United States political scene has been increasing its partisan divide over the years, the normalisation agreements, brokered by the Republican Trump administration, have been met positively by both political parties, including by President-elect Joe Biden. He recalled that he is a son of a family of immigrants of Moroccan origin.
"The state we have lived in for the last 75 years, where Jews and Muslims have been separated, is not a natural state", he said before getting on the plane which was painted with the Hebrew, Arabic and English words for "peace".
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According to BBC, it was the first of 800,000 doses of the vaccine that will be dispensed in the coming weeks. The agency did not say when vaccinations in Switzerland would begin.
Moroccan and Israeli officials also signed accords on linking up aviation and financial systems, visa waivers for holders of diplomatic passports, and water management. "Onboard it, a senior Israel and American delegation and the hopes of the entire nation for the successful promotion of the new Israeli Moroccan friendship", Israel's Foreign Ministry tweeted.
Israel and Morocco marked the breakthrough in diplomatic relations Tuesday with the first direct flight of Israel's national airline, bringing a diplomatic delegation from Tel Aviv to the Moroccan capital of Rabat. This was closed, however, after the Second Palestinian Intifada in 2000.
Tunisia has said it is not interested in establishing diplomatic relations with Israel and its position will not be affected by any worldwide changes.
Morocco has sought to temper the anger by insisting that relations with Israel are not new.
"Not only did intelligence and security cooperation help Israel defend itself in the 1967 Six-Day War and Morocco win its Sahara war a few years later, quiet Moroccan diplomacy proved instrumental in fostering peace between Egypt and Israel", he added.
The Palestinians condemn the agreements as a "stab in the back".
Under the rule of King Mohammed, several programmes have been launched to rehabilitate old Jewish districts, cemeteries and synagogues.