A Singapore court on Thursday handed a 30-month prison sentence to a former private banker with ties to a figure at the center of alleged multibillion-dollar misappropriations at Malaysian state fund 1MDB, the strictest punishment handed out to date as a result of the city-state’s probe of the fund’s finances.

Yeo Jiawei, 33, a former wealth manager at the local branch of Swiss Bank BSI SA, had been convicted a day earlier on four charges of attempting to obstruct the course of justice. Mr. Yeo had fought all the charges...