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If you were seeking the spirit of Picasso in the Middle East, you could study the work of Jawad Selim (1919-1961) and conclude that you had found it. Like many artists of his time, the grandfather of Iraqi modernism was influenced by the Spaniard's Cubism and geometric figures. But Selim was equally, if not more, inspired by Sumerian art, which also rendered subjects in stylized ways. In a work like Baghdadiat (1956), a lively streetscape, it's impossible to tell where modernism begins and the traditional forms of ancient Mesopotamia end.

The painting is currently featured in the inaugural exhibition at Mathaf — the Arab Museum of Modern Art in Doha, Qatar. Titled "Sajjil: A Century of Modern Art," the show runs through October. Sajjil is the imperative form of record in Arabic — a reference to "Sajjil ana Arabi" (Record, I am an Arab), a line from the poem "Identity Card" by Palestinian author Mahmoud Darwish. Selim is one of over a hundred featured artists whose work furthers the exhibition's aim of highlighting art overlooked by modernism's Eurocentric gaze. "Art from the Arab world is not an afterthought or a copy," says Wassan al-Khudhairi, Mathaf's director. "There are multiple threads."

The works on display are entirely drawn from the collection of Sheik Hassan bin Mohamed bin Ali al-Thani, a member of Qatar's royal family and the patron of Mathaf. He spent the past 25 years amassing a vast trove of modern and contemporary Arab art and offering shelter to artists, particularly Iraqis, fleeing unrest. "There are no parallels to a collection like this anywhere," says Salwa Mikdadi, a Palestinian-American curator who works at the Emirates Foundation in Abu Dhabi.

The exhibition comes at a boom time for art in the Gulf, where petrodollars are being poured into a state-led artistic arms race. In Abu Dhabi, an $800 million Frank Gehry — designed branch of the Guggenheim and a satellite of the Louvre, by Jean Nouvel, are being built. In Qatar, a Nouvel-designed museum of local history is in the works. "Commerce has come," Mikdadi says. "Now art and academia need to catch up."

Unlike the Qatari capital's architectural centerpiece, the 2008 I.M. Pei — designed Museum of Islamic Art, Mathaf is located on Doha's dusty periphery in an area called Education City, dotted with newly built colleges and construction sites. The museum is housed, for now, in a former schoolhouse restyled by French architect Jean-François Bodin. Echoing the development taking place all over Qatar, the space is deliberately designed to look impermanent. The entrance is framed by scaffolding and the front desk and lockers made to look like crates. "Nothing is fixed," says al-Khudhairi.

The 260 works in the museum's debut show are arranged according to topics like society and myth, but a uniting preoccupation is the fight for statehood and incumbent matters of identity, history and place. Iraqi artist Dia Azzawi and Kuwaiti sculptor Sami Mohammed capture the pain of the Palestinian people in their artistic renderings of the 1982 massacre at Sabra and Shatila. The central panel of Le Triomphe, a haunting polyptych of the Algerian war by Abdallah Benanteur, has a shape suggestive of both Paris' iconic arch and a weather-beaten tombstone.

The work of Taheya Halim (1919- 2003), a key figure in Egyptian Impressionism, is equally haunting. Her sculpture, The Pyramid, the Civilization, Symbolism Through Ants, consists of a 2.2-m wooden pyramid and looks familiar enough. But as the viewer approaches, dark patches on the pyramid's surface reveal themselves as swarms of ants. The piece, constructed in the 1960s, has been interpreted as a critique of Egypt's Aswan High Dam, a massive public-works project that was a source of controversy on account of the many forced resettlements it involved.

With Egypt once again beset by social tension, Halim's work takes on a fresh relevance — as does Mathaf itself. The museum opened just after the start of the Arab Spring, and its emphasis on agency, critical enquiry and Arab consciousness speaks to the roots of the unrest. Those qualities might seem unlikely in an institution that has a sheik for a patron, but Qatar's royals can afford some liberality, given that their subjects, pacified by years of affluence and steady, if slow, reform, seem more content than others in the region. A reputation for progressive artistic values also does no harm to a tiny but outward-looking state that will host soccer's World Cup in 2022 and seeks to become a global hub. "We recognize we are a work in progress," al-Khudhairi says. She is referring to the museum, but she could equally be talking about Doha, Qatar or contemporary Arab art itself.

• Emily Rauhala
• Mathaf aims to shake up the world of Arab art