The Ambassador of Conscience Award recognises "those who have shown exceptional leadership in the fight for human rights".
Previous award winners include Myanmar opposition leader Aung San Suu Kyi and Irish rock band U2.
The award will be presented at a ceremony in Berlin on 21 May.
Ai told the Associated Press (AP) that he hoped he would be able to attend.
"The Ambassador of Conscience Award is a celebration of those unique individuals who have used their talents to inspire many, many others to take injustice personally," said Salil Shetty, secretary general of Amnesty International.
"That is why both Joan Baez and Ai Weiwei make such worthy recipients; they are an inspiration to thousands more human rights activists, from across Asia to America and beyond."
Baez became involved in civil rights activism in the 1960s and helped establish local Amnesty International groups in San Francisco in the early 1970s.
She said she was "proud" to be honoured, adding: "Amnesty International attracted me because of its founding principle that all human rights abuses and the suffering they create are unacceptable."
An outspoken critic of the Chinese government, Ai was detained for almost three months without charge in 2011. After he was released, he was accused of tax evasion and fined.
On learning of the announcement, Ai said: "I am very privileged to receive this special honour, and shall not fail the encouragement and profound expectation of me with this award."
A Chinese foreign ministry spokeswoman declined to comment on the award to AP in Beijing, but said China hoped Amnesty could regard China "objectively".
The last Ambassador of Conscience Award winners - named in 2013 - were Pakistani teenager Malala Yousafzai and US singer Harry Belafonte.
Chinese dissident artist Ai Weiwei and folk singer Joan Baez are to be jointly presented with Amnesty International's top 2015 human rights award.