Maria Lassnig, Serpentine Gallery, London

As welcomes go, Maria Lassnig's is uncommonly open. Facing the entrance to her Serpentine Gallery show is a self-portrait, painted in 2005, its legs outstretched in an attitude of embrace.

Lassnig's apparently shaved pubic cleft marks the picture's vertical axis, the line passing up between her breasts and eyes. This cleft is also one of three orifices dotted about the picture's composition, the other two being the artist's gaping mouth and the hole in the barrel of a gun. The last is pointed right at us, although Lassnig is pointing another gun, held in her left hand, at her own head. The piece is called Du oder Ich (You or Me), which suggests a relationship between viewer and viewed untypical of self-portraiture as a whole.

Or is it? The most obvious way of reading Du oder Ich is via the good Doctor Freud, the artist's guns being phallic compliments to her female genitals. They may be killing her, but they may equally well kill us; the hole in the gun echoes Lassnig's vagina, possibly the scariest passage in the work and certainly its most embarrassing. Lassnig painted this picture when she was 86. Old ladies' pubes are not an allowable subject for portraiture, especially when painted by the old ladies themselves. In choosing to render herself powerless and vulnerable – naked, suicidal – Lassnig is taking on a power we do not want her to have.

Bound up in her self-portrait, then, is a battle of age and sex, a duality which is spelt out in Freudian symbols and in a formal structure of left-hand-right-hand. If you wonder what lies behind Du oder Ich, remark that when, at the age of 61, Lassnig was eventually made professor of painting in her native Vienna, she was the first woman ever to hold the post in any German-speaking country. If she has an interest in gender, then fair enough.

Lassnig's take on the subject is not simple, though, as the pairing of pictures called The Sports Master and Madonna of the Pastries suggests. For all their his-and-hers bifurcation – boys do gym while girls do cookery – the point of the duo is their similarity.

We've seen the Madonna's pubic cleft before, in Lassnig's self-portrait; but we've seen the Sports Master's threatening mass of flesh in the same place. Being a woman in a man's world is a tricky business, and Lassnig's guide to that world is laced with pain.

What gives her work its extraordinary power is its willingness to own that pain. It's hard not to compare Lassnig with that other battlehorse of the gender wars, Louise Bourgeois. I imagine this comparison would irk both artists, mightily and rightly: just because they're old women doesn't mean they're alike. But Lassnig's exclusion from the mainstream, like Bourgeois', seems to have given her a Tiresias-like ability to see – maybe to be – both sides of the coin: a figure-painter and an abstractionist, viewer and viewed, a man and a woman. Comfortable her work isn't; but then, that is rather its point.

Serpentine Gallery, London W2 (020-7402 6075) to 8 June