There are quite few Rio art museums, I have listed some of the more acknowledged and accessible ones below.

Museu de Arte do Rio (MAR)
Description: Rio’s newest art museum that have exhibitions of various kinds.
Address: Praça Mauá 5, Centro map
Open: Tue-Sun 10h/17h. On Tuesdays free entrance, during summer on this day Mar is open until 19h.
Phone: 3031 2741
Site: Museu de Arte do Rio (MAR)

Museu Nacional de Belas Artes (National Museum of Fine Arts)
Description: A collection of Brazilian art from the 17th to the 20th century. Also international artists including classic European art from 17th to 19th century and some African pieces.
Address: Av Rio Branco 199, Centro map
Open: Tue-Fri 12:30h/18:30h Sat, Sun and holidays 15h/18h.
Phone: 2240-0068
Site: Museu Nacional de Belas Artes

MAM (Museu de Arte Moderna Rio de Janeiro)
Description: Brazilian and international art from the 20th and the 21st century. Rebuilt after catastrophic fire 1978 through donations and purchases. Also houses the Gilberto Chateubriand collection with over 4000 pieces. Well worth a visit and has as a modern art museums should constantly changing exhibitions and events. Has a large art film collection with a cinema as well as workshops. One of the best Rio art museums.
Address: Av. Infante Dom Henrique 85, Parque do Flamengo map
Open: Wed-Sun 11h/18h.
Phone: 2210-2188
Site: MAM

MAC (Museu de Arte Contemporânea de Niterói)
Description: Famous for it´s spectacular design by the Brazilian architect Oscar Niemeyer and the marvelous 360 degree views you get of Rio and Niterói from it. Only opened in 1996 it is already well known around the world. The exhibitions are not all that and the collection is nothing special. The famous shape of the building actually makes it difficult as a exhibition space. For the beauty it is well worth a visit. It is located in Niterói, Rios twin city right across the bay. To get there just catch a ferry from Praça Quinze, arriving on the other side just take a taxi or bus 47B to the museum (just say Mackeeh). Free on Saturdays.
Address: Mirante da Boa Viagem, Boa Viagem map
Open: Tue-Fri, Sun 11h/19h Sat 13h/21h.
Phone: 2620-2481/2620-2400
Site: MAC

MAC in Niterói, one of the more popular Rio art museums

MAC in Niterói

MIAN (International Museum of Naïve Art)
Description Located in a beautiful colonial mansion just by the first station for the Corcovado train. With it’s over 8000 international pieces it´s the biggest museum of naïve art in the world. Exhibiting primitive art recording the history of naïve canvases form the 15th century until today.
Address: R. Cosme Velho 561, Cosme Velho map
Open: Tue-Fri 10h/18h Sat-Sun 10h/17h.
Phone: 2205-8612/2205-8547
Site: MIAN

CCBB (Centro Cultural Banco do Brasil)
Description: This is a dynamic establishment with an wide array of exhibitions and events. Not really one of Rio art museums but is important for the scene. Check out the site below to see what´s on now.
Address: R. Primeiro de Março 66, Centro map
Open: Tue-Sun 10h/21h
Phone: 3808-2020
Site: CCBB

Chacara do Céu
Description:Located in the bohemian neighbourhood Santa Teresa with a spectacular view of Rio de Janeiro. The permanent exhibition features the founder Castro Maya’s personal collection with canvases by Picasso, Dali, and Miró and Brazilian painters like Portinari and Di Cavalcanti.
Address: R. Murtinho Nobre 93, Santa Teresa map
Open Tue-Sun 12h/17h
Phone: 2507-1932/2224-8981/2224-8524
Site: Chacara do Céu

Museu do Índio
Description Although not one of the Rio art museums it has a lot to offer in this area. With it focus on describing the various indigenious cultures of Brazil they also have examples of their art. Unique.
Address: R. das Palmeiras 55, Botafogo map
Open: Tue-Fri 10h/17:30h Sat, Sun and holidays 13h/17h
Phone: 2286-8899
Site: Museu do Índio

Casa do Pontal Arte Popular Brasilieira
Description This folk art museum is exhibiting the results of the life work of a French designer (Jacques van de Beuque). More than 5000 pieces from over 200 artists representing all parts of Brazil. Located in a beautiful summer villa just outside Rio de Janeiro.
Address Estrada do Pontal 3295, Recreio map
Open: Only Sun 9h/17:30h
Phone: 2490-3278/2490-4013
Site: Casa do Pontal Arte Popular Brasilieira