Sisi, the former army chief who ousted Islamist president Mohamed Morsi in July 2013 and launched a deadly crackdown against his supporters, begins Tuesday a visit to Germany at Merkel's invitation.
He will meet the chancellor on Wednesday and other officials, but German parliament speaker Norbert Lammert has called off a meeting he was due to have with Sisi citing human rights abuse.
The five human rights groups, including Amnesty International and Human Rights Watch, highlighted violations in Egypt in a joint statement addressed to Merkel.
"The government headed by President al-Sisi presides over the gravest human rights crisis in Egypt in decades," the statement said.
They urged Merkel "to make clear in your meetings with President al-Sisi... that the nature and extent of Germany's relations with Egypt going forward will depend on the Egyptian authorities taking prompt and concrete measures to put an end to government policies that systematically violate Egypt's obligations under international human rights law as well as the Egyptian Constitution of 2014," the statement said.
It called on Germany to "continue to freeze the transfer of all arms and security related items that could be used for repression until Egyptian authorities have carried out judicial and impartial investigations into the killings of hundreds of protesters by police and security forces, and bring those responsible to justice."
Since Sisi ousted his predecessor Morsi, Egyptian authorities have cracked down on his supporters as well as secular activists.
The crackdown has left hundreds of Morsi supporters dead and thousands jailed, while dozens have been sentenced to death in mass and speedy trials, including Morsi himself.
The sweeping crackdown has likewise seen several top secular activists jailed.
Morsi, Egypt's first freely elected president, and more than 100 co-defendants were sentenced to death by a Cairo court on May 16 for their role in a jail break during the 2011 uprising.
The verdict triggered alarm around the globe with Germany, the United States and several other countries expressing concern.
The open letter to Merkel was also signed by Front Line Defenders, the World Organisation Against Torture and the Euro-Mediterranean Human Rights Network.