They take their data from the WHO, FAO, UNICEF and others if you are talking about the global hunger index.
Here is the FAO with their data for overall malnourishment in a country (its the exact same number GHI uses):
http://www.fao.org/hunger/en/
Their report for Asia:
http://www.fao.org/3/a-i4624e.pdf
More such data (for stunting etc) can be found here:
http://data.unicef.org/topic/nutrition/malnutrition/
GHI literally only compiles 4 published indices by the UN socioeconomic groups and makes an overall composite index of them.
Similarly the base source for my infant mortality, population growth rate, life expectancy etc are from the UN. The World bank just illustrates them on their website like so:
http://data.worldbank.org/indicator/SP.DYN.IMRT.IN?locations=IN-PK
They even say so:
Estimates Developed by the UN Inter-agency Group for Child Mortality Estimation ( UNICEF, WHO, World Bank, UN DESA Population Division ) at childmortality.org.