The partially convertible rupee fell as much as 63.10 to the dollar versus its close of 62.475/485 on Friday. Bond yields also rose tracking gains in US treasury yields.
The 10-year benchmark yield rose 10 basis points to 9.09 percent, a near three-month high.
The US dollar gained against most currencies after an unexpected surge in jobs data, bolstering the case for the Federal Reserve to scale back stimulus as early as next month.