The crime carries a maximum sentence of five years in jail or a maximum fine of 50 million won.
Legal experts, however, said they do not expect the maximum penalty should Lee be found guilty because propofol is less likely to be misused than many other controlled substances.
Lee was convicted in January of bribery and embezzlement and sentenced to 30 months in jail - including a year served before his sentencing. He was paroled in August, with the presidential office calling for public understanding, citing hope that he will help the country produce "semiconductors and vaccines".
After his release, Samsung said it would invest 240 trillion won in the next three years in fields such as chips and biopharmaceuticals. Lee himself has kept a low profile.