A few examples in which racial groups were included or excluded:
Under the Apartheid laws in South Africa, the government was composed of, and elected by, members of the white population. Similarly, under segregation laws in the USA, black people were systematically excluded from government in many states (although this was not done through legal bans, but through "literacy tests" etc.)
"Lebanon has a kind of power-sharing agreement providing for the president to always come from a specific group (namely Maronite Christians) but the president is not elected directly by the people but, like all other relevant office holders (prime minister, speaker of parliament, head of the army, etc.), by the parliament." – Relaxed
These mostly describe one "race" excluding other to maintain their grip on power. There are examples in which a less represented group is guaranteed a role in government in some way:
In Northern Ireland, an assembly is elected, from which an executive is selected. The election process has been chosen to make it very likely that parties representing the Nationalist/Republican and the Unionist will both be represented in the executive, a form of mandatory coalition. The result of this is that the Deputy First Minister has been a representative of the Republican Sinn Fein. Under a voluntary election process, the Unionist parties would have been able to form a coalition to exclude Sinn Fein from government.
In other countries, there have been elections to represent one "race", nation or community. For example Maori election in New Zealand, or the governance of Native American tribes.
The scheme proposed in Singapore looks to be entirely novel (and a huge bureaucratic headache) I can see it coming unstuck with people from mixed backgrounds, the question of how to incorporate people who are not Malay, Chinese, White or Tamil {if these are the four "races"}
