State Bank of India said it had asked a deputy managing director of the bank, Shyamal Acharya, who is under investigation by the CBI in an alleged bribery case, to go on leave.
The police said they had put the deputy managing director under investigation in the case, in which he is alleged to have received Rolex and Omega watches after approving a loan to Worlds Window Group, a metals trading company.
"Incriminating documents recovered during searches are being scrutinised for further investigation," the Central Bureau of Investigation (CBI) said in a statement on Monday.
State-run SBI, the country's biggest bank, said that a committee of two managing directors would investigate the matter internally.
A spokeswoman for Worlds Window Group denied the company paid a bribe to anybody and said it was seeking legal advice.
Reuters was not able to reach Acharya on his mobile phone.
SBI said it is cooperating with the CBI. The bank also said: "We stand committed to probity in our dealings and assure that SBI will continue to hold highest standards of honesty and transparency in its operations."
Indian officials have said the CBI has been scrutinising the 30 biggest defaults at Indian banks for any evidence that borrowers colluded with bankers for personal gain. CBI spokeswoman Kanchan Prasad said the SBI case announced on Monday was not part of that probe.