In April, the ad was given the green light by the ASA after it was shown in cinemas alongside 15-certificate films.
The ad, by Langland, was created for the Medicines and Healthcare Regulatory Authority with Pfizer, and featured on TV screens for the first time last month.
An ASA spokesman said: "The ASA has received 48 complaints about the Pfizer TV ad.
"We are currently assessing the complaints to establish whether or not there are grounds for an investigation."
The ad was developed in response to findings that more than 330,000 men buy prescription-only drugs from unregulated sources, such as internet sites, every year.
In the advertisement, a middle-aged man is seen to take remove a pill from an envelope. Seconds later, he reaches into his mouth to pull out a huge rat, tail first.