HTML text input field with currency symbol

Use a parent .input-icon div. Optionally add .input-icon-right.

<div class="input-icon">
  <input type="text">
  <i>$</i>
</div>

<div class="input-icon input-icon-right">
  <input type="text">
  <i>€</i>
</div>

Align the icon vertically with transform and top, and set pointer-events to none so that clicks focus on the input. Adjust the padding and width as appropriate:

.input-icon {
  position: relative;
}

.input-icon > i {
  position: absolute;
  display: block;
  transform: translate(0, -50%);
  top: 50%;
  pointer-events: none;
  width: 25px;
  text-align: center;
  font-style: normal;
}

.input-icon > input {
  padding-left: 25px;
  padding-right: 0;
}

.input-icon-right > i {
  right: 0;
}

.input-icon-right > input {
  padding-left: 0;
  padding-right: 25px;
  text-align: right;
}

Unlike the accepted answer, this will retain input validation highlighting, such as a red border when there's an error.

JSFiddle usage example with Bootstrap and Font Awesome

You can wrap your input field into a span, which you position:relative;. Then you add with :before content:"€" your currency symbol and make it position:absolute. Working JSFiddle

HTML

<span class="input-symbol-euro">
    <input type="text" />
</span>

CSS

.input-symbol-euro {
    position: relative;
}
.input-symbol-euro input {
    padding-left:18px;
}
.input-symbol-euro:before {
    position: absolute;
    top: 0;
    content:"€";
    left: 5px;
}

Update If you want to put the euro symbol either on the left or the right side of the text box. Working JSFiddle

HTML

<span class="input-euro left">
    <input type="text" />
</span>
<span class="input-euro right">
    <input type="text" />
</span>

CSS

 .input-euro {
     position: relative;
 }
 .input-euro.left input {
     padding-left:18px;
 }
 .input-euro.right input {
     padding-right:18px;
     text-align:end; 
 }

 .input-euro:before {
     position: absolute;
     top: 0;
     content:"€";
 }
 .input-euro.left:before {
     left: 5px;
 }
 .input-euro.right:before {
     right: 5px;
 }

Consider simulating an input field with a fixed prefix or suffix using a span with a border around a borderless input field. Here's a basic kickoff example:

.currencyinput {
    border: 1px inset #ccc;
}
.currencyinput input {
    border: 0;
}

<span class="currencyinput">$<input type="text" name="currency"></span>