If you are using a fully connected network (aka an MLP) and images with one channel (grey scale) and 100 x 100 = 10,000 pixels, then yes, MLP would have 10k inputs and 10k x N 1 trainable weights in the first layer (as noted by Neil Slater). If you have a color image with 3 channels, e.g. RGB, then you can expect 3 times as many weights because there are 3 times as many values used to represent the image.
A convolutional neural network is a common architecture for analyzing images. For a 100x100 (10k) pixel image, the input layer might have 3x3x1x32 = 288 weights (for 1 channel) or 3x3x3x32 = 864 weights in the first layer, much less than 10k x N 1 from a fully connected network. This would transform your image into a 98x98x32 size image. The main point is that you would have 3x3 weights per input channel per output channel at each layer, instead of 10k weights per input channel per output channel. CNNs also give you some invariance properties that are usually nice in machine learning with images.
For images in general, having a lot of weights is normal. ImageNet (linked above) has 60 million weights to train. Typically special hardware, like a GPU is used to handle this many weights. If you are using just a CPU, your model may not train well in any reasonable amount of time, i.e. years.