Parts of this could be causal from income to health, as being less able to afford the best medical care can matter, and overcrowded housing is associated with the lower tail of the income distribution. Other parts can be causal from health to income, where poor health means you can't work.
But still other parts could be due to common underlying causes for both health and income. Linda Gottfredson pointed to IQ as a fundamental underlying cause: correcting for IQ knocks back the association between health and income. Higher IQ people know how to follow doctors' orders and also earn more.
Here's the latest from Current Biology:
Individuals with lower socio-economic status (SES) are at increased risk of physical and mental illnesses and tend to die at an earlier age [1, 2, 3]. Explanations for the association between SES and health typically focus on factors that are environmental in origin . However, common SNPs have been found collectively to explain around 18% of the phenotypic variance of an area-based social deprivation measure of SES . Molecular genetic studies have also shown that common physical and psychiatric diseases are partly heritable . It is possible that phenotypic associations between SES and health arise partly due to a shared genetic etiology. We conducted a genome-wide association study (GWAS) on social deprivation and on household income using 112,151 participants of UK Biobank. We find that common SNPs explain 21% of the variation in social deprivation and 11% of household income. Two independent loci attained genome-wide significance for household income, with the most significant SNP in each of these loci being rs187848990 on chromosome 2 and rs8100891 on chromosome 19. Genes in the regions of these SNPs have been associated with intellectual disabilities, schizophrenia, and synaptic plasticity. Extensive genetic correlations were found between both measures of SES and illnesses, anthropometric variables, psychiatric disorders, and cognitive ability. These findings suggest that some SNPs associated with SES are involved in the brain and central nervous system. The genetic associations with SES obviously do not reflect direct causal effects and are probably mediated via other partly heritable variables, including cognitive ability, personality, and health.