Wendy Fawell, 50, was at the Ariana Grande concert with her daughter Charlotte and friends.
She is believed to have been near the exit area shortly before the blast and has not been heard from since.
Sharing a picture on Facebook, Charlotte said: “Please share! Wendy Fawell hasn’t been seen since just before the incident at Manchester arena! Don’t know if she has her phone on her or not, police are aware, just if anyone has seen her! Thankyou x”
Since then the appeal has been shared widely on social media.
Leeds Underdogs ARL told its Twitter followers: “Friends of ours are looking for a Wendy Fawell-New. If anyone know if she is safe, please get back to us.”
It appears another of her party was injured during the attack.
Daniel Frank wrote on Facebook: “We know that at least one of our members was caught up in this. Caroline, we are all thinking of you and you have a mass of support behind you.
“Worryingly, Caroline’s friend (and my friend’s auntie) Wendy Fawell is still missing. Please do share and pray that she’s safe.”
Leeds North West MP Greg Mulholland said: “Deeply worried that Wendy Fawell who lived in Otley is still unnaccounted for in last night’s atrocity. I am also aware that at least one other person from Otley has been injured and is receiving treatment today.
“Thoughts and prayers with family and friends and all those caught up in this awful and evil act.”
Wendy, who is from Guiseley originally, now lives in Otley.
A vigil will take place in the town at Buttercross at 7.30pm tonight as the community awaits further news.
The gathering has been organised with the consent of her family.