It is known that many animals posess the ability to sense magnetic fields (magnetoreception), a well-known example are migratory birds. Humans are generally considered to lack such a mechanism.
From the article "A behavioral perspective on the biophysics of the light-dependent magnetic compass: a link between directional and spatial perception?":
The intervening years have provided a wealth of evidence that the
magnetic sense is present in taxonomically diverse groups of animals
(Wiltschko and Wiltschko, 1995). For example, among mammals there is
evidence for magnetic sensitivity in mice, hamsters, rats, mole rats,
bats, cows and deer (Olcese et al., 1985; Burda et al., 1990; Kimchi
and Terkel, 2001; Deutschlander et al., 2003; Muheim et al., 2006a;
Thalau et al., 2006; Begall et al., 2008; Holland et al., 2008).
Indeed, animals that do not have a magnetic sense (humans are widely
assumed to fall in this category) may be the exception, rather than
There are some studies by Robin Baker, but they are cited as controversial in the newer articles I found on the topic.
From "Human cryptochrome exhibits light-dependent magnetosensitivity":
Humans are widely assumed not to have a magnetic sense3. For example,
the extensive behavioural studies by Robin Baker11,12,13,14,15,
suggesting a link between non-visual navigation and magnetoreception
in humans, are controversial. However, there is consistent evidence of
an influence of geomagnetic fields on the light sensitivity of the
human visual system16,17.
In this article the authors show that humans posess one protein that can potentially sense magnetic fields:
Our results show that hCRY2, the prototype type 2 CRY18,19, has the
molecular capability to function in a light-dependent magnetoreception
system, either as a light-sensitive magnetosensor or as part of a
magnetosensing pathway. However, we do not yet know whether this
capability is translated into a downstream biological response in the
So far there is no convincing data that humans can sense magnetic fields, but there are some results that merit some further investigation. But even if we can sense magnetic fields, I would strongly doubt any medical effects of such magnets unless they are shown in a clinical trial.