A spokeswoman for the DTI said the office had issued summonses last Friday against Andrew Tuckey, the former deputy chairman of the bank, and nine other former directors including Peter Norris, the former chief executive.
The DTI is also seeking to ban Ian Hopkins, the former head of risk at Barings, and Ron Baker, the immediate boss of Nick Leeson, the trader based in Singapore who broke the bank by running up unauthorised trading losses of more than pounds 800m.
Leeson was jailed in Singapore in 1995 after admitting charges of fraud.
The DTI action is being taken under the Company Directors Disqualification Act, which can lead to bans from directly or indirectly forming, promoting or managing companies for 15 years.
The former directors have been the subject of disciplinary procedures by the Securities and Futures Authority (SFA), the City watchdog.
Some of them, including Mr Norris, have been banned from working in the City in management roles for periods of up to three years.
But Mr Baker succeeded in fighting an attempt by the regulator to ban him after a disciplinary tribunal at the SFA cleared him of four out of five charges.
He is appealing against the one charge in which the tribunal found against him.
Mr Hopkins fought a high-profile campaign to clear his name in which he said he had acted as a "whistleblower". However, he refused to recognise the SFA's disciplinary proceedings and it is believed that a tribunal has barred him from taking management roles in the City.
None of the former directors is currently employed in the City with the exception of Mr Tuckey, an experienced corporate finance specialist who remained at Barings in a consultancy role after it was bought by ING, the Dutch financial services group.
He is now working with Phoenix, a corporate finance boutique which was sold recently to Donald Lufkin & Jenrette, the US bank.
Last year the SFA formally cleared Mr Tuckey and Peter Baring, the bank's former chairman, of responsibility for the collapse of the 233-year-old merchant bank.
Yesterday Mr Norris declined to comment while Mr Hopkins, Mr Tuckey and Mr Baker could not be reached.
Some of the former directors also face court action brought by Coopers & Lybrand, the accountancy firm which audited the accounts of Barings.
Coopers & Lybrand last year issued writs against a number of former Barings bosses, blaming them for the bank's spectacular collapse in 1995.
Most of the money lost as a result of the bank's collapse was incurred by the holders of Barings bonds, who are continuing their fight to recoup their losses.