Rosie Garthwaite & Ian Anderson
The rights group found the apps were carrying out live or near-live tracking of users' locations by uploading GPS co-ordinates to a central server.
It urged the Gulf states to stop using them in their current forms.
Norway has halted the roll-out of its app because of similar concerns.
The country's data protection authority said the app represented a disproportionate intrusion into users' privacy given the low rate of infection there.
Researchers at Amnesty's Security Lab carried out a technical analysis of 11 apps in Algeria, Bahrain, France, Iceland, Israel, Kuwait, Lebanon, Norway, Qatar, Tunisia and the United Arab Emirates.
Bahrain's "BeAware Bahrain" and Kuwait's "Shlonik" stood out, along with Norway's "Smittestopp", as being among the most alarming mass surveillance tools, according a report published on Tuesday.
Most contact-tracing apps rely solely on Bluetooth signals, but Bahrain and Kuwait's capture location data through GPS and upload this to a central database, tracking the movements of users in real time.
The researchers say Bahraini and Kuwaiti authorities would be able to easily link this sensitive personal information to an individual, as users are required to register with a national ID number. Other countries' contact tracing apps anonymise users.
Accessing such data could help authorities tackle Covid-19, but Claudio Guarnieri, head of Amnesty's Security Lab, said the apps were "running roughshod over people's privacy, with highly invasive surveillance tools which go far beyond what is justified".
Mr Guarnieri added: "They are essentially broadcasting the locations of users to a government database in real time - this is unlikely to be necessary and proportionate in the context of a public health response. Technology can play a useful role in contact tracing to contain Covid-19, but privacy must not be another casualty as governments rush to roll out apps."
Mohammed al-Maskati, a Bahraini activist who is the Middle East digital protection co-ordinator for the human rights group Front Line Defenders, said there was also a concern the information collected by the apps might be shared with third parties.
Bahrain's app was linked to a television show called "Are You At Home?", which offered prizes to users who stayed at home during Ramadan.
The issues uncovered by Amnesty's investigation are particularly alarming given that the human rights records of Gulf governments are poor.
"When you equip a repressive state with the means to surveil an entire population - whether it's in the name of public safety or not - you can be certain that it's only going to enhance their means of control and repression to then track down dissidents or anyone that they consider to be a public threat. And in a lot of places like the Gulf, that means activists," says Sarah Aoun, chief technologist at privacy campaign organisation Open Tech Fund.
There is also a concern that the technology will continue to be used after the threat of the coronavirus recedes, Ms Aoun adds.
"Historically, there's been no incentive for governments to limit their overreach into people's privacy. On the contrary, if you take a look at 9/11 and the aftermath of that, it essentially ushered a new era of surveillance in the name of protecting citizens. And this time is no different."
Mr Maskati says critics will be unable to rely on regulatory oversight bodies in Gulf states for protection.
"If privacy is violated in a country like Norway, I can resort to regional tools such as the European Court of Human Rights and European Committee of Social Rights. But in our region there is not any such tool. On the contrary, resorting to local authorities may present an additional risk."
Bahrain and Kuwait did not respond to the BBC's request for comment.