Mr Singh is due to visit at least one hospital and to discuss security in the wake of Tuesday's blasts, which killed nearly 180 people.
His visit comes after Pakistani President Pervez Musharraf offered to help India find those responsible.
Suspicions that Pakistan-based militants may have been involved have raised tensions between the two states.
Indian security officials have suggested that the Mumbai bombings bore the hallmarks of Lashkar-e-Toiba, a Kashmiri militant group operating from Pakistan.
But the group has not been directly accused and has denied responsibility.
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