Interesting question, and potentially has many possible solutions. Here is my approach, basically first calculate where the label '0' is, then draw a new axis there using absolute coordinates, and finally put the image there:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import pylab as pl
A = np.random.random(size=(5,5))
fig, ax = plt.subplots(1, 1)
xl, yl, xh, yh=np.array(ax.get_position()).ravel()
w=xh-xl
h=yh-yl
xp=xl+w*0.1 #if replace '0' label, can also be calculated systematically using xlim()
size=0.05
img=mpimg.imread('microblog.png')
ax.matshow(A)
ax1=fig.add_axes([xp-size*0.5, yh, size, size])
ax1.axison = False
imgplot = ax1.imshow(img,transform=ax.transAxes)
plt.savefig('temp.png')
