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I don't know if this method will pass museum standards, but as an old sewing expert I would repair it with a linen patch on the back. There are a number of fabric glues on the market which you would apply to your linen patch (make sure you get a permanent glue, not a temporary one). Then press your patch onto the back side of the painting and smooth it with your fingers to flatten it. You may need to use an iron to help you flatten the fibers on the front. But do this from the back side with a press cloth. Trim any loose threads from the rip before you do this.
As I said before, this may not be the archival method, but it's what I would do, and I've done it many many times in my old business (custom bedrooms).
Jean
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