Visit Rwanda and the Premier League club signed the multi-year deal on Tuesday, with media reports putting the value at about £20 million ($26 million) per year.
Amnesty International UK said the partnership risked helping Rwanda sportswash its human rights record and cited allegations surrounding the country's role in the conflict in neighbouring Democratic Republic of Congo, BBC Sport reported.
The Rwandan government has regularly denied allegations that it backs any rebel groups operating in Congo.
"It's not new that Rwanda is using sportswashing to deflect attention from its terrible human rights record," Amnesty UK's head of campaigns, Felix Jakens, told BBC Sport.
"Aston Villa should be well aware that Rwanda is seeking to leverage this partnership to create positive PR ... Rwanda's sportswashing needs to be called out, and we'd like Aston Villa and the Premier League to play their part in this."
Reuters has contacted Aston Villa, Visit Rwanda and Amnesty International for comment.
The African nation's tourism board already has sponsorship agreements with Atletico Madrid and PSG, as well as US sports teams including the Los Angeles Clippers and Los Angeles Rams.
It previously had an eight-year sleeve sponsorship deal with Arsenal that ended last season. That deal sparked protests from sections of the London club's support.
Villa had been looking to replace its previous sponsor Betano after Premier League clubs agreed to end front-of-shirt sponsorship by betting firms.
