Nintendo reported that a patch will release tomorrow for Super Smash Brothers 3DS that will allow Ammibo to work .

This feature will only work if you have a New 3DS console which releases on February 13th. No word if an attachment will be released any time soon to allow ammibo to work for standard 3DS models.

The patch / update for Super Smash brothers 3DS will be on the Nintendo e-shop to download.

Update:

This is what Nintendo says is in the update:

Update Details:

This update also includes the previous game updates.

Share mode has been added.
- Users will be able to post photos, replay data, and Mii Fighter data to the official server to share with other users around the world. Users will also be able to search and download the content as well.
  *Users can only post their own content. Content posted to the server will be deleted after 30 days.
- Users will be able to share and exchange photos, replay data, and Mii Fighter data with users on their 3DS Friend List.
  *Content will be received when the Nintendo 3DS is connected to the Internet
  *It may take some time to receive the data
  *Content uploaded to the server will be deleted from the server after 30 days.
- Users will be able to post photos to Miiverse from within the game
amiibo functionality has been added to New Nintendo 3DS XL
Users can tap their amiibo figure to the touchscreen to transform them into “figure players (FP)” to battle, train, and level-up their FP.
*FPs that were trained in Super Smash Bros. for Wii U can be used in Super Smash Bros. for Nintendo 3DS.
*Nintendo 3DS/XL systems will be compatible with amiibo functionality using a peripheral device scheduled to launch in 2015 and the software update that will follow.
In order to let you play the game more comfortably, we have also fixed some issues.

Please note: Once users install the update data (Ver. 1.0.5), they will no longer be able to play local multiplayer with users without the update installed. Additionally, any replay data that was saved prior to the update will no longer be playable.
Users will be required to download this update prior to using the software's online multiplayer features.

I couldn't find the ammibo menus like how it is on Wii U version but I don't have New 3DS. I don't have link to location to where replays are shared either, but I'm glad this update has this feature.