A special court under the Central Bureau of Investigation (CBI) ordered the 82-year-old Singh, billionaire Kumar Mangalam Birla and another official to appear on April 8, the court said in an order.
"I am upset, but this is a part of life," a visibly distressed Singh told reporters in parliament, where he sits in the Rajya Sabha. It is rare but not unknown for former Indian prime ministers to be called into court.
Known for his personal integrity and humble lifestyle, Singh has not been charged with any crime but is being investigated for criminal breach of trust, criminal conspiracy, cheating and corruption, a prosecution lawyer said on condition of anonymity.
The CBI had earlier excluded Singh from the investigation. His Congress party called the summons a backlash against its opposition to economic reforms that Prime Minister Narendra Modi wants to push through parliament.
In the past, the Supreme Court has accused the CBI of acting on the wishes of the government.
The summons coincided with a debate in the Rajya Sabha on a bill to allow coal-field auctions. Environment Minister Prakash Javadekar said the issue was a blot on Congress and called on the party to end its opposition to the bill.
"I hope reason will prevail," Javadekar said. He denied any vendetta or political interference in the judicial process.
The maximum sentence for criminal breach of trust is life imprisonment. Singh said he was evaluating his legal options, which include seeking a stay on the summons from a higher court.
The mild-mannered economist implemented 1990s free-market reforms that unshackled India from its socialist past. Recognisable in his trademark blue turban, glasses and beard, he played a prominent role managing the 2008 financial crisis.
His second term at the helm of a Congress-led coalition was mired in corruption scandals and accusations that party leader Sonia Gandhi called the shots, tarnishing his image.
"We have done nothing wrong and we have nothing to hide," said Ambika Soni, a senior Congress leader close to the Gandhis.
The Gandhi lineage stretches back to India's first prime minister, Jawaharlal Nehru. The family ruled for much of the period from independence in 1947.
Most coal block awards made by Singh's government, which ran India for a decade, were overturned late last year by the Supreme Court, which ruled the process illegal.
The case known as "Coalgate" came to light in 2012 after a government auditor said the exchequer had lost up to $33 billion due to collusion between officials and private firms to depress the cost of coal-field awards.
Modi, who ousted Singh in an election last May, issued an executive order to re-auction the fields in a process key to reducing India's dependence on coal imports. He needs to pass legislation to make the decree permanent, however the Supreme Court has made clear that auctioned fields will not be affected if the decree lapses.
Auctions of the first 32 blocks have brought in a projected $32 billion, Coal Secretary Anil Swarup told Reuters.
The summons relates to the allocation of a coal field in 2005 to Hindalco Industries, part of the $40 billion Aditya Birla Group. Kumar Mangalam Birla is the chairman of the group.
Judge Bharat Parashar said in the summons "a well planned conspiracy was hatched" to award Hindalco the field after Birla actively lobbied Singh, who was at the time acting as coal minister. The document does not establish which politicians or officials may have benefited but said Singh's office showed "undue interest" in the matter.
Accused of manipulating the government, Hindalco said in a statement that it made its case during its bid to get access to the coal field "in a transparent and lawful manner".
Shares in Hindalco, an aluminium company, fell by 5 percent to their lowest in nearly a year - extending falls over the past week to nearly 20 percent.
Modi, who promised a "Congress-free India" in his election campaign, was visiting the Seychelles as news of the summons broke, posting photos on Facebook of the tropical islands.