An official with Syria's Internal Security Forces said the Islamic State group was behind the bombings. The extremist group has not claimed the attacks.
Security forces carried out raids in the Syrian capital and the surrounding areas, and "succeeded in dismantling the entire cell responsible" for the bombings, the Interior Ministry said in a statement.
On Tuesday, explosive devices were planted in a garbage bin and a parked car during Macron's landmark visit to Syria, a country rebuilding from years of civil war.
Macron, who was in the presidential palace when the blasts happened, was not harmed and continued with his meeting with Syrian President Ahmad al-Sharaa.
The explosions killed one person and wounded 36 others, according to the final casualty toll announced by Syria's Ministry of Health.
Last week, an explosive device detonated in a cafe near Damascus' main judicial complex, killing at least 10 people and wounding more than 20.
The explosions are a challenge to al-Sharaa, who has pushed to assert full control over Syria. He has appealed to minorities sceptical of his government's Islamist-led rule and sought to win support of Western governments concerned about his past leadership of the formerly al-Qaeda-linked group known as Hayat Tahrir al-Sham.
His government has promised political and economic reform after decades of autocratic rule of the Assad family, which ended when former President Bashar Assad was ousted in an insurgent offensive in December 2024 led by al-Sharaa.
The nearly 14-year civil war in Syria killed nearly half a million people and displaced millions, leaving much devastation and infrastructure in ruins. While other nations and businesses have made large investment pledges, the country still needs hundreds of billions of dollars to rebuild and lift millions out of poverty.
Meanwhile, France has finally returned 23 Syrian archaeological treasures that remained in the country for about 15 years after being loaned for an exhibition.
The artefacts, flown aboard Macron's presidential aircraft on Tuesday and returned to Syria's National Museum, include Roman bronze objects, Byzantine and Islamic-era pieces and a richly coloured mosaic panel that once adorned the Umayyad Mosque.
The collection was loaned in 2011 to an exhibition of Syrian antiquities at the Arab World Institute in Paris - but remained in France after diplomatic ties between the two countries were severed under Assad's rule.
At the National Museum, curator Nivine Saadeddine said the returned collection spans some of the most significant periods of Syrian civilisation.
Syria's cultural heritage suffered extensive damage during the country's years of conflict.
Ancient cities, including the UNESCO World Heritage site of Palmyra, were heavily damaged, while landmarks such as the medieval Crusader fortress of Crac des Chevaliers bear scars from years of fighting. IS militants also destroyed temples, tombs and monumental sculptures in Palmyra, considering them symbols of idolatry, while trafficked antiquities became a lucrative source of revenue for armed groups.
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