Building on garry's answer, you can have Wikipedia parse the info box into HTML for you via the rvparse parameter like so:
http://en.wikipedia.org/w/api.php?action=query&prop=revisions&rvprop=content&format=json&titles=Scary%20Monsters%20and%20Nice%20Sprites&rvsection=0&rvparse
Note that neither method will return just the info box. But from the HTML content, you can extract (via, e.g., Beautiful Soup) the table with class infobox.
In Python, you do something like the following
resp = requests.get(url).json()
page_one = next(iter(resp['query']['pages'].values()))
revisions = page_one.get('revisions', [])
html = next(iter(revisions[0].values()))
# Now parse the HTML